JCAP02(2016)002

ournal of Cosmology and Astroparticle PhysicsAn IOP and SISSA journalJ

Signatures from scalar dark matterwith a vector-like quark mediator

Federica Giacchinoa Alejandro Ibarrab Laura Lopez Honorezc

Michel HG Tytgata and Sebastian Wildb

aService de Physique Theorique CP225 Universite Libre de BruxellesBld du Triomphe 1050 Brussels BelgiumbPhysik-Department T30d Technische Universitat MunchenJames-Franck-Straszlige D-85748 Garching GermanycVrije Universiteit Brussel and The International Solvay InstitutesPleinlaan 2 B-1050 Brussels Belgium

E-mail federicagiacchinoulbacbe ibarratumde llopezhovubacbemtytgatulbacbe sebastianwildphtumde

Received December 2 2015Accepted January 18 2016Published February 1 2016

Abstract We present a comprehensive study of a model where the dark matter is composedof a singlet real scalar that couples to the Standard Model predominantly via a Yukawainteraction with a light quark and a colored vector-like fermion A distinctive feature of thisscenario is that thermal freeze-out in the early universe may be driven by annihilation bothinto gluon pairs at one-loop (gg) and by virtual internal Bremsstrahlung of a gluon (qqg)Such a dark matter candidate may also be tested through direct and indirect detection and atthe LHC viable candidates have either a mass nearly degenerate with that of the fermionicmediator or a mass above about 2 TeV

Keywords dark matter theory dark matter experiments particle physics - cosmology con-nection

ArXiv ePrint 151104452

Article funded by SCOAP3 Content from this work may be usedunder the terms of the Creative Commons Attribution 30 License

Any further distribution of this work must maintain attribution to the author(s)and the title of the work journal citation and DOI

doi1010881475-7516201602002

JCAP02(2016)002

Contents

1 Introduction 1

2 Dark matter relic density 3

21 Perturbative analysis 3

22 Sommerfeld corrections to the co-annihilation processes 5

23 Results of the relic density calculation 7

3 Direct detection constraints 8

4 Constraints from searches at the LHC 11

41 Production of mediator pairs 12

42 Constraints derived from the multijet ATLAS analysis 13

5 Indirect detection constraints 16

6 Conclusion 19

1 Introduction

In recent years dark matter in the form of Weakly Interacting Massive Particles (WIMPs)has become the leading particle physics candidate The most salient feature of WIMP darkmatter is the prediction of a relic abundance via thermal freeze-out that is in rough agreementwith the measured value when the WIMP annihilation cross section into Standard Model(SM) particles is of the order of 1 pb thus suggesting parameters in the dark sector (WIMPmass and couplings) comparable to those in the electroweak sector Furthermore manyparticle physics models addressing the electroweak hierarchy problem contain among manynew states a dark matter candidate with the characteristics of a WIMP While the lack ofexperimental evidence for these extra states is disfavoring some of these schemes the freeze-out mechanism still stands as one of the most natural and elegant mechanisms to explain theorigin of the dark matter

An exciting feature of the WIMP dark matter paradigm and arguably one of the reasonsfor its popularity is the possibility of detecting experimental signals of processes inducedby the weak coupling of the dark matter with the Standard Model particles Numerousexperiments are currently searching for dark matter particles either through direct andindirect detection or at colliders and are already providing fairly stringent limits on therates of the processes relevant for each search strategy Unfortunately the limits on thefundamental parameters of the model which can be derived from the null searches as wellas the complementarity among the various search strategies are highly model dependentOn the other hand the main features of the dark matter phenomenology of a given modelcan be in many instances captured by considering only a subset of the new fields and newparameters namely by considering ldquosimplified modelsrdquo

The simplest among all the simplified WIMP models is to extend the Standard Modelwith a singlet real scalar S and with a discrete Z2 symmetry unbroken in the electroweak

ndash 1 ndash

JCAP02(2016)002

vacuum under which the singlet scalar is odd while all the Standard Model fields are even [1ndash4] and which ensures the dark matter stability1 The singlet scalar interacts with the Stan-dard Model particles only through a renormalizable quartic coupling to the Brout-Englert-Higgs doublet (Higgs for short)

L sup minus1

2m2SS

2 minus 1

2λS2HdaggerH (11)

thus the model only contains one new field and two new parameters mS and λ thephenomenology of this very simple scenario has been studied in many works (see forinstance [12ndash18])

In this paper we will investigate the impact on the dark matter phenomenology ofextending this model by one vector-like fermionic field ψ also odd under the discrete Z2

symmetry and which couples to the singlet scalar S and a right-handed SM fermion fR viaa Yukawa interaction (the discussion for a left-handed SM fermion is completely analogous)The Lagrangian of the Z2-odd fermionic sector reads

L sup minusy S ψfR + ψ(i D minusmψ)ψ + hc (12)

The gauge invariance of the Yukawa term implies that the fermion must be a SU(2)L singletand have the same hypercharge as the SM fermion it couples to Besides the vector-likenature of the fermion ensures the cancellation of the gauge anomalies2 From a more funda-mental perspective notice that this model is also a simplified version of a scenario with largeextra dimensions (see [19] and references therein)

As we will argue when the strength of the ldquovector-like portalrdquo interaction is larger thanthe strength of the ldquoHiggs-portalrdquo interaction the phenomenology of the model presents quitedistinctive characteristics which make this model rather unique The phenomenology of thevector-like portal interaction has been partially discussed in eg [19ndash27] The case in whichfR is a light lepton was first discussed in [23 24] There it was shown that the annihilation ofS through the portal of eq (12) into two SM fermions is dominated in the limit mf mS by the d-wave thus σv prop v4 and that the virtual internal Bremsstrahlung (VIB) in theannihilation may lead to rather intense gamma ray spectral features (see also [28ndash32] forrelevant literature on VIB in an analogous framework with Majorana dark matter) Furtherphenomenological aspects of this ldquoleptophilicrdquo scenario were studied in [26] and [27] Inparticular [26] analyzed constraints both from indirect detection through gamma rays andfrom colliders

In the present work we will study the possibility that the dark matter couples to alight quark assuming for simplicity minimal flavour violation An interesting feature of

1Other parity assignments are possible For instance stability of scalar DM may be explained throughembedding in SO(10) using matter parity P = (minus)3(BminusL) which is a remnant of a gauge symmetry [5] Inthis framework SM fermions are as usual in a 16SM (odd under P ) while the SM Higgs is in 10H (even) IfP is unbroken a possibility is to embed scalar DM in a 16DM which contains a singlet scalar and a scalardoublet (aka inert doublet) Either one may play the role of DM [5] Notice that Yukawas of the form ofeq (12) may be obtained by coupling the 16DM to 16SM through fermions in the 10rarr 5oplus 5 which containsa SU(2)L singlet vector-like quark akin to the dR as well as a leptonic SU(2)L doublet Of course morework would be necessary to make this a phenomenologically viable framework For recent works along thisdirection see [6ndash11]

2Taking ψ chiral instead requires introducing more fields but is otherwise an obvious extension (with apossible caveat regarding the mass of the ψ which may have to come from couplings to the Higgs and thusmay not be arbitrarily large)

ndash 2 ndash

JCAP02(2016)002

this scenario is that due to the d-wave suppression of the annihilation rate into a quark-antiquark pair the relic abundance is driven either by the annihilation of S into two gluons3

(gg) and into VIB of a gluon (qqg) or by the co-annihilation of the colored ψ particleThe latter process can be significantly affected by the exchange of gluons between the non-relativistic fermion mediators a phenomenon that may lead to Sommerfeld enhancement ofthe annihilation cross-section The correct description of the phenomenology of the modelthen requires the inclusion of higher-order effects as well as non-perturbative effects

The fact that the fermionic mediator ψ is colored also opens interesting possibilities fordirect detection and collider searches4 Specifically we consider the constraints set by theLUX [35] experiment and the prospects for detection by XENON1T [36] To this end we takeinto account the effective coupling at one-loop of the S to gluons recently calculated in [37]Furthermore the model can be tested at colliders through the production of the mediatorparticles ψ which are both colored and electrically charged and which subsequently decayproducing a signature of two or more jets plus missing transverse energy ET Altogetherdirect detection and production of the fermionic mediator at colliders put the strongest con-straints on our scenario Finally we also consider indirect searches in particular constraintson continuum gamma-ray signals from dwarf spheroidal galaxies (dSphs) and gamma-rayspectral features based on data from Fermi-LAT and HESS and on anti-protons in cos-mic rays using the PAMELA data While overall less constraining these data sets will allowus to close a narrow region of the parameter space that otherwise would be left open bycurrent direct and collider searches Similar analyses applied to other dark matter scenarioshave been pursued in refs [38ndash43]

This article is organized as follows We first determine in section 2 the dark matterrelic abundance taking into account higher-order processes involving gluons as well as theSommerfeld enhancement for co-annihilation of the fermionic mediator Then we study insections 3 4 and 5 the constraints from direct searches collider searches and indirect searchesrespectively We finally draw our conclusions in section 6

2 Dark matter relic density

As will be shown below the relic dark matter abundance is determined either by the one-loop annihilation into gluon pairs (gg) or the VIB in the annihilation (qqg) or by the co-annihilation with the colored partner We first discuss the perturbative aspects of the anni-hilation and then the Sommerfeld effects in the co-annihilation processes associated to theexchange of gluons between particles in initial states

21 Perturbative analysis

We will focus on the scenario where the vector-like portal interaction dominates over theHiggs portal interaction namely we assume that the quartic coupling is small enough to playno role In this case the lowest order dark matter annihilation channel is SS rarr qq with the

3The possibility that the annihilation into gluon pairs could drive the dark matter freeze-out was previouslyconsidered in [33] using a model-independent effective operator framework The present model provides anexplicit UV realization of this scenario

4As the couplings we consider violate flavour symmetry it is legitimate to ask whether our scenario maybe made consistent with constraints on flavour changing neutral processes This issue has been addressedin [34] where two mechanisms to suppress such processes (degeneracy and alignment) are discussed As thesemechanisms directly apply to our model we do not repeat the argument but refer to [34] for more details

ndash 3 ndash

JCAP02(2016)002

S

S

q

q

ψ

S

S

q

q

V

ψ

S

S

q

q

q

ψ

V

V prime

Figure 1 Annihilation channels of the dark matter particle S during freeze-out In the limit mq rarr 0the annihilation channel SS rarr qq shown in the left panel is d-wave suppressed (see text for details)and the higher order processes shown in the central and right panel dominate the total annihilationcross section For each process we only show one representative diagram

annihilation cross-section given by

σv 3y4

4πm2S(1 + r2)2

(m2q

m2S

minus 2

3

m2qv

2(1 + 2r2)

m2S(1 + r2)2

+v4

15 (1 + r2)2

) (21)

where we have kept only the leading terms in an expansion in mq mS and relative velocityv Here r equiv mψmS gt 1 denotes the mass ratio between the vector-like mediator and thedark matter particle It follows that in the limit mq rarr 0 which is relevant for the case ofdark matter coupling to a light quark the annihilation of dark matter into a pair of quarks isd-wave suppressed [23 24] While the absence of the s-wave component in the limit mq rarr 0is analogous to the well-known helicity suppression in the case of annihilation of a Majoranafermion pair into light fermions the vanishing of the p-wave component is unique to theannihilation of two real scalar particles see [24] for a more detailed discussion

Due to the strong suppression of the tree-level two-to-two cross-section it is crucialto take into account higher-order effects in the calculation of the relic density There aretwo relevant classes of higher-order processes which contribute to the total annihilation crosssection SS rarr qqV ie the internal Bremsstrahlung of a gauge boson V with V = γ Z g aswell as SS rarr V V prime the one-loop annihilation of dark matter into a pair of gauge bosons V V primeRepresentative diagrams for these higher-order annihilation channels are shown in figure 1together with the tree-level annihilation process SS rarr qq In contrast to eq (21) the higher-order processes feature a non-vanishing s-wave component in the limit mq rarr 0 at the priceof being suppressed by an additional gauge coupling and reduced phase space in the case ofinternal Bremsstrahlung or by a loop suppression factor for annihilation into gauge bosonsAnalytical expressions of the corresponding cross sections can be found in [23 24 26 27]

To calculate the relic density we employ the micrOMEGAS4 package [44] which wemodified in order to include the additional annihilation channels5 We find that in the wholeparameter space either the internal Bremsstrahlung processes or the one-loop annihilationsgive a larger contribution to the total annihilation cross section at freeze-out than the anni-hilation into qq given by eq (21) Due to the different scaling with the mass ratio r of thetwo higher-order processes namely σv prop 1r8 for internal Bremsstrahlung and σv prop 1r4

5For the higher-order processes we only include the s-wave contribution to the annihilation cross sectionin the calculation of the relic density

ndash 4 ndash

JCAP02(2016)002

for one-loop annihilations (see [23 24 26 27]) the former dominates the total annihilationcross section for small mass ratios (concretely r 25) while the latter is more importantfor large mass ratios

Furthermore if the fermionic mediator is close in mass to the dark matter particleco-annihilation processes ie annihilations of S and ψ ψ and ψ or ψ and ψ [45] canplay a significant role in the calculation of the relic density As is well known the co-annihilation channels have rates exponentially suppressed when ∆m equiv mψminusmS Tfo yetfor small mass splittings they can dominate over the self-annihilation channels which havein this model suppressed rates We employ micrOMEGAS4 in order to include all relevantco-annihilation processes in our numerical calculation and we find that co-annihilationsgive a contribution to ΩDM of at least 5 for mass splittings r 15 135 125 at mS =10 GeV 100 GeV 1 TeV respectively It is important to note that some of the co-annihilationprocesses as eg ψψ rarr gg are purely given by gauge interactions in particular they areindependent of the Yukawa coupling y Consequently if mS and r are small enough theseannihilation channels can suppress the relic density below the observed value irrespectivelyof the value of y6

For the parts of the parameter space where co-annihilations are not relevant the relicdensity is set by the higher-order processes introduced above and consequently rather largeYukawa couplings are typically necessary for matching the observed relic density As it willbe discussed in the rest of this work this implies potentially observable signals in direct andindirect detection as well as in the production of the mediator at colliders

22 Sommerfeld corrections to the co-annihilation processes

The annihilation of two colored particles (for our purposes with initial states ψψ ψψ or ψψ)can be significantly affected by the non-perturbative Sommerfeld effect induced by the mul-tiple exchange of gluons in the initial state For the quantitative treatment of the Sommerfeldeffect we closely follow the method presented in [43 46] which we briefly recapitulate here

Expanding the perturbative annihilation cross section as

σpert =a

v+ bv +O(v2) (22)

the Sommerfeld corrected cross section can be written as

σSomm = S0a

v+ S1bv +O(v2) (23)

Here Sl is the Sommerfeld factor associated with the partial wave l which takes theform [47 48]

S0 =minus2παv

1minus exp(2παv) Slgt0 = S0 times

lprod

k=1

(1 +

α2

v2k2

) (24)

In these expressions v is the relative velocity between the two annihilating particles and thecoupling α parametrizes the strength of the effective QCD potential between the annihilatingparticles For two annihilating particles with representations R and Rprime under SU(3)c thenon-abelian matrix potential between the particles can be diagonalized by decomposing the

6Co-annihilation still requires that S harr ψ transitions on SM particles of the thermal bath are in equilibriumat the time of freeze-out We have checked that this is the case provided y amp 10minus4

ndash 5 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

vacuum under which the singlet scalar is odd while all the Standard Model fields are even [1ndash4] and which ensures the dark matter stability1 The singlet scalar interacts with the Stan-dard Model particles only through a renormalizable quartic coupling to the Brout-Englert-Higgs doublet (Higgs for short)

L sup minus1

2m2SS

2 minus 1

2λS2HdaggerH (11)

thus the model only contains one new field and two new parameters mS and λ thephenomenology of this very simple scenario has been studied in many works (see forinstance [12ndash18])

In this paper we will investigate the impact on the dark matter phenomenology ofextending this model by one vector-like fermionic field ψ also odd under the discrete Z2

symmetry and which couples to the singlet scalar S and a right-handed SM fermion fR viaa Yukawa interaction (the discussion for a left-handed SM fermion is completely analogous)The Lagrangian of the Z2-odd fermionic sector reads

L sup minusy S ψfR + ψ(i D minusmψ)ψ + hc (12)

The gauge invariance of the Yukawa term implies that the fermion must be a SU(2)L singletand have the same hypercharge as the SM fermion it couples to Besides the vector-likenature of the fermion ensures the cancellation of the gauge anomalies2 From a more funda-mental perspective notice that this model is also a simplified version of a scenario with largeextra dimensions (see [19] and references therein)

As we will argue when the strength of the ldquovector-like portalrdquo interaction is larger thanthe strength of the ldquoHiggs-portalrdquo interaction the phenomenology of the model presents quitedistinctive characteristics which make this model rather unique The phenomenology of thevector-like portal interaction has been partially discussed in eg [19ndash27] The case in whichfR is a light lepton was first discussed in [23 24] There it was shown that the annihilation ofS through the portal of eq (12) into two SM fermions is dominated in the limit mf mS by the d-wave thus σv prop v4 and that the virtual internal Bremsstrahlung (VIB) in theannihilation may lead to rather intense gamma ray spectral features (see also [28ndash32] forrelevant literature on VIB in an analogous framework with Majorana dark matter) Furtherphenomenological aspects of this ldquoleptophilicrdquo scenario were studied in [26] and [27] Inparticular [26] analyzed constraints both from indirect detection through gamma rays andfrom colliders

In the present work we will study the possibility that the dark matter couples to alight quark assuming for simplicity minimal flavour violation An interesting feature of

1Other parity assignments are possible For instance stability of scalar DM may be explained throughembedding in SO(10) using matter parity P = (minus)3(BminusL) which is a remnant of a gauge symmetry [5] Inthis framework SM fermions are as usual in a 16SM (odd under P ) while the SM Higgs is in 10H (even) IfP is unbroken a possibility is to embed scalar DM in a 16DM which contains a singlet scalar and a scalardoublet (aka inert doublet) Either one may play the role of DM [5] Notice that Yukawas of the form ofeq (12) may be obtained by coupling the 16DM to 16SM through fermions in the 10rarr 5oplus 5 which containsa SU(2)L singlet vector-like quark akin to the dR as well as a leptonic SU(2)L doublet Of course morework would be necessary to make this a phenomenologically viable framework For recent works along thisdirection see [6ndash11]

2Taking ψ chiral instead requires introducing more fields but is otherwise an obvious extension (with apossible caveat regarding the mass of the ψ which may have to come from couplings to the Higgs and thusmay not be arbitrarily large)

ndash 2 ndash

JCAP02(2016)002

this scenario is that due to the d-wave suppression of the annihilation rate into a quark-antiquark pair the relic abundance is driven either by the annihilation of S into two gluons3

(gg) and into VIB of a gluon (qqg) or by the co-annihilation of the colored ψ particleThe latter process can be significantly affected by the exchange of gluons between the non-relativistic fermion mediators a phenomenon that may lead to Sommerfeld enhancement ofthe annihilation cross-section The correct description of the phenomenology of the modelthen requires the inclusion of higher-order effects as well as non-perturbative effects

The fact that the fermionic mediator ψ is colored also opens interesting possibilities fordirect detection and collider searches4 Specifically we consider the constraints set by theLUX [35] experiment and the prospects for detection by XENON1T [36] To this end we takeinto account the effective coupling at one-loop of the S to gluons recently calculated in [37]Furthermore the model can be tested at colliders through the production of the mediatorparticles ψ which are both colored and electrically charged and which subsequently decayproducing a signature of two or more jets plus missing transverse energy ET Altogetherdirect detection and production of the fermionic mediator at colliders put the strongest con-straints on our scenario Finally we also consider indirect searches in particular constraintson continuum gamma-ray signals from dwarf spheroidal galaxies (dSphs) and gamma-rayspectral features based on data from Fermi-LAT and HESS and on anti-protons in cos-mic rays using the PAMELA data While overall less constraining these data sets will allowus to close a narrow region of the parameter space that otherwise would be left open bycurrent direct and collider searches Similar analyses applied to other dark matter scenarioshave been pursued in refs [38ndash43]

This article is organized as follows We first determine in section 2 the dark matterrelic abundance taking into account higher-order processes involving gluons as well as theSommerfeld enhancement for co-annihilation of the fermionic mediator Then we study insections 3 4 and 5 the constraints from direct searches collider searches and indirect searchesrespectively We finally draw our conclusions in section 6

2 Dark matter relic density

As will be shown below the relic dark matter abundance is determined either by the one-loop annihilation into gluon pairs (gg) or the VIB in the annihilation (qqg) or by the co-annihilation with the colored partner We first discuss the perturbative aspects of the anni-hilation and then the Sommerfeld effects in the co-annihilation processes associated to theexchange of gluons between particles in initial states

21 Perturbative analysis

We will focus on the scenario where the vector-like portal interaction dominates over theHiggs portal interaction namely we assume that the quartic coupling is small enough to playno role In this case the lowest order dark matter annihilation channel is SS rarr qq with the

3The possibility that the annihilation into gluon pairs could drive the dark matter freeze-out was previouslyconsidered in [33] using a model-independent effective operator framework The present model provides anexplicit UV realization of this scenario

4As the couplings we consider violate flavour symmetry it is legitimate to ask whether our scenario maybe made consistent with constraints on flavour changing neutral processes This issue has been addressedin [34] where two mechanisms to suppress such processes (degeneracy and alignment) are discussed As thesemechanisms directly apply to our model we do not repeat the argument but refer to [34] for more details

ndash 3 ndash

JCAP02(2016)002

S

S

q

q

ψ

S

S

q

q

V

ψ

S

S

q

q

q

ψ

V

V prime

Figure 1 Annihilation channels of the dark matter particle S during freeze-out In the limit mq rarr 0the annihilation channel SS rarr qq shown in the left panel is d-wave suppressed (see text for details)and the higher order processes shown in the central and right panel dominate the total annihilationcross section For each process we only show one representative diagram

annihilation cross-section given by

σv 3y4

4πm2S(1 + r2)2

(m2q

m2S

minus 2

3

m2qv

2(1 + 2r2)

m2S(1 + r2)2

+v4

15 (1 + r2)2

) (21)

where we have kept only the leading terms in an expansion in mq mS and relative velocityv Here r equiv mψmS gt 1 denotes the mass ratio between the vector-like mediator and thedark matter particle It follows that in the limit mq rarr 0 which is relevant for the case ofdark matter coupling to a light quark the annihilation of dark matter into a pair of quarks isd-wave suppressed [23 24] While the absence of the s-wave component in the limit mq rarr 0is analogous to the well-known helicity suppression in the case of annihilation of a Majoranafermion pair into light fermions the vanishing of the p-wave component is unique to theannihilation of two real scalar particles see [24] for a more detailed discussion

Due to the strong suppression of the tree-level two-to-two cross-section it is crucialto take into account higher-order effects in the calculation of the relic density There aretwo relevant classes of higher-order processes which contribute to the total annihilation crosssection SS rarr qqV ie the internal Bremsstrahlung of a gauge boson V with V = γ Z g aswell as SS rarr V V prime the one-loop annihilation of dark matter into a pair of gauge bosons V V primeRepresentative diagrams for these higher-order annihilation channels are shown in figure 1together with the tree-level annihilation process SS rarr qq In contrast to eq (21) the higher-order processes feature a non-vanishing s-wave component in the limit mq rarr 0 at the priceof being suppressed by an additional gauge coupling and reduced phase space in the case ofinternal Bremsstrahlung or by a loop suppression factor for annihilation into gauge bosonsAnalytical expressions of the corresponding cross sections can be found in [23 24 26 27]

To calculate the relic density we employ the micrOMEGAS4 package [44] which wemodified in order to include the additional annihilation channels5 We find that in the wholeparameter space either the internal Bremsstrahlung processes or the one-loop annihilationsgive a larger contribution to the total annihilation cross section at freeze-out than the anni-hilation into qq given by eq (21) Due to the different scaling with the mass ratio r of thetwo higher-order processes namely σv prop 1r8 for internal Bremsstrahlung and σv prop 1r4

5For the higher-order processes we only include the s-wave contribution to the annihilation cross sectionin the calculation of the relic density

ndash 4 ndash

JCAP02(2016)002

for one-loop annihilations (see [23 24 26 27]) the former dominates the total annihilationcross section for small mass ratios (concretely r 25) while the latter is more importantfor large mass ratios

Furthermore if the fermionic mediator is close in mass to the dark matter particleco-annihilation processes ie annihilations of S and ψ ψ and ψ or ψ and ψ [45] canplay a significant role in the calculation of the relic density As is well known the co-annihilation channels have rates exponentially suppressed when ∆m equiv mψminusmS Tfo yetfor small mass splittings they can dominate over the self-annihilation channels which havein this model suppressed rates We employ micrOMEGAS4 in order to include all relevantco-annihilation processes in our numerical calculation and we find that co-annihilationsgive a contribution to ΩDM of at least 5 for mass splittings r 15 135 125 at mS =10 GeV 100 GeV 1 TeV respectively It is important to note that some of the co-annihilationprocesses as eg ψψ rarr gg are purely given by gauge interactions in particular they areindependent of the Yukawa coupling y Consequently if mS and r are small enough theseannihilation channels can suppress the relic density below the observed value irrespectivelyof the value of y6

For the parts of the parameter space where co-annihilations are not relevant the relicdensity is set by the higher-order processes introduced above and consequently rather largeYukawa couplings are typically necessary for matching the observed relic density As it willbe discussed in the rest of this work this implies potentially observable signals in direct andindirect detection as well as in the production of the mediator at colliders

22 Sommerfeld corrections to the co-annihilation processes

The annihilation of two colored particles (for our purposes with initial states ψψ ψψ or ψψ)can be significantly affected by the non-perturbative Sommerfeld effect induced by the mul-tiple exchange of gluons in the initial state For the quantitative treatment of the Sommerfeldeffect we closely follow the method presented in [43 46] which we briefly recapitulate here

Expanding the perturbative annihilation cross section as

σpert =a

v+ bv +O(v2) (22)

the Sommerfeld corrected cross section can be written as

σSomm = S0a

v+ S1bv +O(v2) (23)

Here Sl is the Sommerfeld factor associated with the partial wave l which takes theform [47 48]

S0 =minus2παv

1minus exp(2παv) Slgt0 = S0 times

lprod

k=1

(1 +

α2

v2k2

) (24)

In these expressions v is the relative velocity between the two annihilating particles and thecoupling α parametrizes the strength of the effective QCD potential between the annihilatingparticles For two annihilating particles with representations R and Rprime under SU(3)c thenon-abelian matrix potential between the particles can be diagonalized by decomposing the

6Co-annihilation still requires that S harr ψ transitions on SM particles of the thermal bath are in equilibriumat the time of freeze-out We have checked that this is the case provided y amp 10minus4

ndash 5 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

this scenario is that due to the d-wave suppression of the annihilation rate into a quark-antiquark pair the relic abundance is driven either by the annihilation of S into two gluons3

(gg) and into VIB of a gluon (qqg) or by the co-annihilation of the colored ψ particleThe latter process can be significantly affected by the exchange of gluons between the non-relativistic fermion mediators a phenomenon that may lead to Sommerfeld enhancement ofthe annihilation cross-section The correct description of the phenomenology of the modelthen requires the inclusion of higher-order effects as well as non-perturbative effects

The fact that the fermionic mediator ψ is colored also opens interesting possibilities fordirect detection and collider searches4 Specifically we consider the constraints set by theLUX [35] experiment and the prospects for detection by XENON1T [36] To this end we takeinto account the effective coupling at one-loop of the S to gluons recently calculated in [37]Furthermore the model can be tested at colliders through the production of the mediatorparticles ψ which are both colored and electrically charged and which subsequently decayproducing a signature of two or more jets plus missing transverse energy ET Altogetherdirect detection and production of the fermionic mediator at colliders put the strongest con-straints on our scenario Finally we also consider indirect searches in particular constraintson continuum gamma-ray signals from dwarf spheroidal galaxies (dSphs) and gamma-rayspectral features based on data from Fermi-LAT and HESS and on anti-protons in cos-mic rays using the PAMELA data While overall less constraining these data sets will allowus to close a narrow region of the parameter space that otherwise would be left open bycurrent direct and collider searches Similar analyses applied to other dark matter scenarioshave been pursued in refs [38ndash43]

This article is organized as follows We first determine in section 2 the dark matterrelic abundance taking into account higher-order processes involving gluons as well as theSommerfeld enhancement for co-annihilation of the fermionic mediator Then we study insections 3 4 and 5 the constraints from direct searches collider searches and indirect searchesrespectively We finally draw our conclusions in section 6

2 Dark matter relic density

As will be shown below the relic dark matter abundance is determined either by the one-loop annihilation into gluon pairs (gg) or the VIB in the annihilation (qqg) or by the co-annihilation with the colored partner We first discuss the perturbative aspects of the anni-hilation and then the Sommerfeld effects in the co-annihilation processes associated to theexchange of gluons between particles in initial states

21 Perturbative analysis

We will focus on the scenario where the vector-like portal interaction dominates over theHiggs portal interaction namely we assume that the quartic coupling is small enough to playno role In this case the lowest order dark matter annihilation channel is SS rarr qq with the

3The possibility that the annihilation into gluon pairs could drive the dark matter freeze-out was previouslyconsidered in [33] using a model-independent effective operator framework The present model provides anexplicit UV realization of this scenario

4As the couplings we consider violate flavour symmetry it is legitimate to ask whether our scenario maybe made consistent with constraints on flavour changing neutral processes This issue has been addressedin [34] where two mechanisms to suppress such processes (degeneracy and alignment) are discussed As thesemechanisms directly apply to our model we do not repeat the argument but refer to [34] for more details

ndash 3 ndash

JCAP02(2016)002

S

S

q

q

ψ

S

S

q

q

V

ψ

S

S

q

q

q

ψ

V

V prime

Figure 1 Annihilation channels of the dark matter particle S during freeze-out In the limit mq rarr 0the annihilation channel SS rarr qq shown in the left panel is d-wave suppressed (see text for details)and the higher order processes shown in the central and right panel dominate the total annihilationcross section For each process we only show one representative diagram

annihilation cross-section given by

σv 3y4

4πm2S(1 + r2)2

(m2q

m2S

minus 2

3

m2qv

2(1 + 2r2)

m2S(1 + r2)2

+v4

15 (1 + r2)2

) (21)

where we have kept only the leading terms in an expansion in mq mS and relative velocityv Here r equiv mψmS gt 1 denotes the mass ratio between the vector-like mediator and thedark matter particle It follows that in the limit mq rarr 0 which is relevant for the case ofdark matter coupling to a light quark the annihilation of dark matter into a pair of quarks isd-wave suppressed [23 24] While the absence of the s-wave component in the limit mq rarr 0is analogous to the well-known helicity suppression in the case of annihilation of a Majoranafermion pair into light fermions the vanishing of the p-wave component is unique to theannihilation of two real scalar particles see [24] for a more detailed discussion

Due to the strong suppression of the tree-level two-to-two cross-section it is crucialto take into account higher-order effects in the calculation of the relic density There aretwo relevant classes of higher-order processes which contribute to the total annihilation crosssection SS rarr qqV ie the internal Bremsstrahlung of a gauge boson V with V = γ Z g aswell as SS rarr V V prime the one-loop annihilation of dark matter into a pair of gauge bosons V V primeRepresentative diagrams for these higher-order annihilation channels are shown in figure 1together with the tree-level annihilation process SS rarr qq In contrast to eq (21) the higher-order processes feature a non-vanishing s-wave component in the limit mq rarr 0 at the priceof being suppressed by an additional gauge coupling and reduced phase space in the case ofinternal Bremsstrahlung or by a loop suppression factor for annihilation into gauge bosonsAnalytical expressions of the corresponding cross sections can be found in [23 24 26 27]

To calculate the relic density we employ the micrOMEGAS4 package [44] which wemodified in order to include the additional annihilation channels5 We find that in the wholeparameter space either the internal Bremsstrahlung processes or the one-loop annihilationsgive a larger contribution to the total annihilation cross section at freeze-out than the anni-hilation into qq given by eq (21) Due to the different scaling with the mass ratio r of thetwo higher-order processes namely σv prop 1r8 for internal Bremsstrahlung and σv prop 1r4

5For the higher-order processes we only include the s-wave contribution to the annihilation cross sectionin the calculation of the relic density

ndash 4 ndash

JCAP02(2016)002

for one-loop annihilations (see [23 24 26 27]) the former dominates the total annihilationcross section for small mass ratios (concretely r 25) while the latter is more importantfor large mass ratios

Furthermore if the fermionic mediator is close in mass to the dark matter particleco-annihilation processes ie annihilations of S and ψ ψ and ψ or ψ and ψ [45] canplay a significant role in the calculation of the relic density As is well known the co-annihilation channels have rates exponentially suppressed when ∆m equiv mψminusmS Tfo yetfor small mass splittings they can dominate over the self-annihilation channels which havein this model suppressed rates We employ micrOMEGAS4 in order to include all relevantco-annihilation processes in our numerical calculation and we find that co-annihilationsgive a contribution to ΩDM of at least 5 for mass splittings r 15 135 125 at mS =10 GeV 100 GeV 1 TeV respectively It is important to note that some of the co-annihilationprocesses as eg ψψ rarr gg are purely given by gauge interactions in particular they areindependent of the Yukawa coupling y Consequently if mS and r are small enough theseannihilation channels can suppress the relic density below the observed value irrespectivelyof the value of y6

For the parts of the parameter space where co-annihilations are not relevant the relicdensity is set by the higher-order processes introduced above and consequently rather largeYukawa couplings are typically necessary for matching the observed relic density As it willbe discussed in the rest of this work this implies potentially observable signals in direct andindirect detection as well as in the production of the mediator at colliders

22 Sommerfeld corrections to the co-annihilation processes

The annihilation of two colored particles (for our purposes with initial states ψψ ψψ or ψψ)can be significantly affected by the non-perturbative Sommerfeld effect induced by the mul-tiple exchange of gluons in the initial state For the quantitative treatment of the Sommerfeldeffect we closely follow the method presented in [43 46] which we briefly recapitulate here

Expanding the perturbative annihilation cross section as

σpert =a

v+ bv +O(v2) (22)

the Sommerfeld corrected cross section can be written as

σSomm = S0a

v+ S1bv +O(v2) (23)

Here Sl is the Sommerfeld factor associated with the partial wave l which takes theform [47 48]

S0 =minus2παv

1minus exp(2παv) Slgt0 = S0 times

lprod

k=1

(1 +

α2

v2k2

) (24)

In these expressions v is the relative velocity between the two annihilating particles and thecoupling α parametrizes the strength of the effective QCD potential between the annihilatingparticles For two annihilating particles with representations R and Rprime under SU(3)c thenon-abelian matrix potential between the particles can be diagonalized by decomposing the

6Co-annihilation still requires that S harr ψ transitions on SM particles of the thermal bath are in equilibriumat the time of freeze-out We have checked that this is the case provided y amp 10minus4

ndash 5 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

S

S

q

q

ψ

S

S

q

q

V

ψ

S

S

q

q

q

ψ

V

V prime

Figure 1 Annihilation channels of the dark matter particle S during freeze-out In the limit mq rarr 0the annihilation channel SS rarr qq shown in the left panel is d-wave suppressed (see text for details)and the higher order processes shown in the central and right panel dominate the total annihilationcross section For each process we only show one representative diagram

annihilation cross-section given by

σv 3y4

4πm2S(1 + r2)2

(m2q

m2S

minus 2

3

m2qv

2(1 + 2r2)

m2S(1 + r2)2

+v4

15 (1 + r2)2

) (21)

where we have kept only the leading terms in an expansion in mq mS and relative velocityv Here r equiv mψmS gt 1 denotes the mass ratio between the vector-like mediator and thedark matter particle It follows that in the limit mq rarr 0 which is relevant for the case ofdark matter coupling to a light quark the annihilation of dark matter into a pair of quarks isd-wave suppressed [23 24] While the absence of the s-wave component in the limit mq rarr 0is analogous to the well-known helicity suppression in the case of annihilation of a Majoranafermion pair into light fermions the vanishing of the p-wave component is unique to theannihilation of two real scalar particles see [24] for a more detailed discussion

Due to the strong suppression of the tree-level two-to-two cross-section it is crucialto take into account higher-order effects in the calculation of the relic density There aretwo relevant classes of higher-order processes which contribute to the total annihilation crosssection SS rarr qqV ie the internal Bremsstrahlung of a gauge boson V with V = γ Z g aswell as SS rarr V V prime the one-loop annihilation of dark matter into a pair of gauge bosons V V primeRepresentative diagrams for these higher-order annihilation channels are shown in figure 1together with the tree-level annihilation process SS rarr qq In contrast to eq (21) the higher-order processes feature a non-vanishing s-wave component in the limit mq rarr 0 at the priceof being suppressed by an additional gauge coupling and reduced phase space in the case ofinternal Bremsstrahlung or by a loop suppression factor for annihilation into gauge bosonsAnalytical expressions of the corresponding cross sections can be found in [23 24 26 27]

To calculate the relic density we employ the micrOMEGAS4 package [44] which wemodified in order to include the additional annihilation channels5 We find that in the wholeparameter space either the internal Bremsstrahlung processes or the one-loop annihilationsgive a larger contribution to the total annihilation cross section at freeze-out than the anni-hilation into qq given by eq (21) Due to the different scaling with the mass ratio r of thetwo higher-order processes namely σv prop 1r8 for internal Bremsstrahlung and σv prop 1r4

5For the higher-order processes we only include the s-wave contribution to the annihilation cross sectionin the calculation of the relic density

ndash 4 ndash

JCAP02(2016)002

for one-loop annihilations (see [23 24 26 27]) the former dominates the total annihilationcross section for small mass ratios (concretely r 25) while the latter is more importantfor large mass ratios

Furthermore if the fermionic mediator is close in mass to the dark matter particleco-annihilation processes ie annihilations of S and ψ ψ and ψ or ψ and ψ [45] canplay a significant role in the calculation of the relic density As is well known the co-annihilation channels have rates exponentially suppressed when ∆m equiv mψminusmS Tfo yetfor small mass splittings they can dominate over the self-annihilation channels which havein this model suppressed rates We employ micrOMEGAS4 in order to include all relevantco-annihilation processes in our numerical calculation and we find that co-annihilationsgive a contribution to ΩDM of at least 5 for mass splittings r 15 135 125 at mS =10 GeV 100 GeV 1 TeV respectively It is important to note that some of the co-annihilationprocesses as eg ψψ rarr gg are purely given by gauge interactions in particular they areindependent of the Yukawa coupling y Consequently if mS and r are small enough theseannihilation channels can suppress the relic density below the observed value irrespectivelyof the value of y6

For the parts of the parameter space where co-annihilations are not relevant the relicdensity is set by the higher-order processes introduced above and consequently rather largeYukawa couplings are typically necessary for matching the observed relic density As it willbe discussed in the rest of this work this implies potentially observable signals in direct andindirect detection as well as in the production of the mediator at colliders

22 Sommerfeld corrections to the co-annihilation processes

The annihilation of two colored particles (for our purposes with initial states ψψ ψψ or ψψ)can be significantly affected by the non-perturbative Sommerfeld effect induced by the mul-tiple exchange of gluons in the initial state For the quantitative treatment of the Sommerfeldeffect we closely follow the method presented in [43 46] which we briefly recapitulate here

Expanding the perturbative annihilation cross section as

σpert =a

v+ bv +O(v2) (22)

the Sommerfeld corrected cross section can be written as

σSomm = S0a

v+ S1bv +O(v2) (23)

Here Sl is the Sommerfeld factor associated with the partial wave l which takes theform [47 48]

S0 =minus2παv

1minus exp(2παv) Slgt0 = S0 times

lprod

k=1

(1 +

α2

v2k2

) (24)

In these expressions v is the relative velocity between the two annihilating particles and thecoupling α parametrizes the strength of the effective QCD potential between the annihilatingparticles For two annihilating particles with representations R and Rprime under SU(3)c thenon-abelian matrix potential between the particles can be diagonalized by decomposing the

6Co-annihilation still requires that S harr ψ transitions on SM particles of the thermal bath are in equilibriumat the time of freeze-out We have checked that this is the case provided y amp 10minus4

ndash 5 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

for one-loop annihilations (see [23 24 26 27]) the former dominates the total annihilationcross section for small mass ratios (concretely r 25) while the latter is more importantfor large mass ratios

Furthermore if the fermionic mediator is close in mass to the dark matter particleco-annihilation processes ie annihilations of S and ψ ψ and ψ or ψ and ψ [45] canplay a significant role in the calculation of the relic density As is well known the co-annihilation channels have rates exponentially suppressed when ∆m equiv mψminusmS Tfo yetfor small mass splittings they can dominate over the self-annihilation channels which havein this model suppressed rates We employ micrOMEGAS4 in order to include all relevantco-annihilation processes in our numerical calculation and we find that co-annihilationsgive a contribution to ΩDM of at least 5 for mass splittings r 15 135 125 at mS =10 GeV 100 GeV 1 TeV respectively It is important to note that some of the co-annihilationprocesses as eg ψψ rarr gg are purely given by gauge interactions in particular they areindependent of the Yukawa coupling y Consequently if mS and r are small enough theseannihilation channels can suppress the relic density below the observed value irrespectivelyof the value of y6

For the parts of the parameter space where co-annihilations are not relevant the relicdensity is set by the higher-order processes introduced above and consequently rather largeYukawa couplings are typically necessary for matching the observed relic density As it willbe discussed in the rest of this work this implies potentially observable signals in direct andindirect detection as well as in the production of the mediator at colliders

22 Sommerfeld corrections to the co-annihilation processes

The annihilation of two colored particles (for our purposes with initial states ψψ ψψ or ψψ)can be significantly affected by the non-perturbative Sommerfeld effect induced by the mul-tiple exchange of gluons in the initial state For the quantitative treatment of the Sommerfeldeffect we closely follow the method presented in [43 46] which we briefly recapitulate here

Expanding the perturbative annihilation cross section as

σpert =a

v+ bv +O(v2) (22)

the Sommerfeld corrected cross section can be written as

σSomm = S0a

v+ S1bv +O(v2) (23)

Here Sl is the Sommerfeld factor associated with the partial wave l which takes theform [47 48]

S0 =minus2παv

1minus exp(2παv) Slgt0 = S0 times

lprod

k=1

(1 +

α2

v2k2

) (24)

In these expressions v is the relative velocity between the two annihilating particles and thecoupling α parametrizes the strength of the effective QCD potential between the annihilatingparticles For two annihilating particles with representations R and Rprime under SU(3)c thenon-abelian matrix potential between the particles can be diagonalized by decomposing the

6Co-annihilation still requires that S harr ψ transitions on SM particles of the thermal bath are in equilibriumat the time of freeze-out We have checked that this is the case provided y amp 10minus4

ndash 5 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

direct product RotimesRprime = sumQQ as a sum of irreducible representations Q This gives rise to

the effective potential (see eg [46])

V (r) =α

r=αsr

1

2(CQ minus CR minus CRprime) (25)

where we evaluate αs at an energy scale equal to the momenta of the annihilating particlesp = mv2 and the Ci are the quadratic Casimir operators associated with the representa-tion i For the model under consideration we will be interested in processes involving theannihilation of colored fermion triplets giving rise to 3otimes 3 = 1oplus 8 and 3otimes 3 = 6oplus 3 Theassociated Casimir operators are given by C1 = 0 C3 = C3 = 43 C6 = 103 and C8 = 3The effective QCD potentials then read

V3otimes3 =αs(micro = p)

r

minus4

3(1)

1

6(8)

and V3otimes3 =αs(micro = p)

r

minus2

3(3)

1

3(6)

(26)

and are hence attractive for the singlet and the anti-triplet two particles states while they are

repulsive for the others In the following we will refer to S(1)l S

(8)l S

(3)l S

(6)l for the Som-

merfeld factors defined in eq (24) evaluated for a coupling α = αstimesminus43 16minus23 13respectively

As the Sommerfeld enhancement depends on the initial color state one has to deter-mine the relative probabilities of annihilation in a given color state separately for everyannihilation channel As discussed in [46] using tensor decomposition one can show thatψψ rarr gg occurs with probability 27 (57) through a singlet (octet) state giving rise to thetotal Sommerfeld factor7

S(gg)l =

2

7S

(1)l +

5

7S

(8)l (27)

For the annihilation channel ψψ rarr qq due to the Yukawa interaction of eq (12) a similarcalculation yields

S(qq)l =

1

3S

(3)l +

2

3S

(6)l (28)

On the other hand the annihilations of ψψ into γg Zg (γγ γZ ZZWWZh) correspondto a pure octet (singlet) initial state due to color conservation The associated Sommerfeldfactors are thus given by

S(γgZg)l = S

(8)l S

(γγγZZZWWZh)l = S

(1)l (29)

Finally we also consider the co-annihilation process ψψ rarr qq When the dark matterhas a tree-level Yukawa interaction with the quark q the co-annihilation process is mediatedby the t-channel exchange of a fermionic mediator as well as by the s-channel exchange of agluon If this is not the case only the s-channel process is relevant As a consequence theSU(3)c representation of the initial state crucially depends on the concrete quark producedin the final state Namely if only the s-channel mediates the co-annihilation the initial stateis a pure octet On the other hand if the s- and t-channels interfere the initial state is

7These relative probabilities have been calculated in the limit v rarr 0 ie for Slgt0 they are in principle(slightly) different We have checked that the error associated to the simplification of applying the sameprobabilities also for l gt 0 is negligible The same argument also holds for the other annihilation channels

ndash 6 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5 10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1Coupling to uR

no thermal relic

ythermal gt 6

001

01

1

6

001

01

1

6y

10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5 10 102 103 10410minus4

10minus3

10minus2

10minus1

1

5

mS [GeV]

y

Coupling to uR

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 2 Viable parameter space of the scalar dark matter model In the left panel the colorgradient corresponds to values of the Yukawa coupling giving rise to the observed relic abundancewhile in the right panel the color gradient corresponds to values of r minus 1 (with r = mψmS) leadingto ΩDMh

2 012 Note that for definiteness these plots are for the case of dark matter coupling touR however the results for coupling to dR are practically identical (see discussion in the text)

combination of singlet and octet representations therefore the total Sommerfeld factor cannot be expressed in a simple form analogously to eqs (27)ndash(29) instead we fully decomposethe squared matrix element into the part corresponding to a singlet and an octet initial state

and multiply each contribution with S(1)l and S

(8)l respectively

23 Results of the relic density calculation

In this work we consider the case of dark matter coupling either to the right-handed up-quark uR or to the right-handed down-quark dR Both for the annihilation and the co-annihilation processes the dominant contribution to the annihilation cross section ariseseither from the Yukawa interaction or from the QCD interaction the latter being identical forcoupling to uR and dR Hence up to sub-percent corrections arising from diagrams involvingelectromagnetic or weak couplings the Yukawa coupling corresponding to the observed relicdensity is identical in both of these scenarios Note however that we fully include all sub-leading effects in our numerical calculations

In figure 2 we show the viable parameter space in the plane spanned by the dark mattermass mS and the relative mass difference r minus 1 as well as in the plane spanned by mS andthe Yukawa coupling y The color gradient corresponds to the value of the Yukawa couplingin the left panel and to the value of r minus 1 in the right panel required to match the observedrelic abundance ΩDMh

2 012 In both panels the region at small mS andor small rie the dark grey in the left panel corresponds to parameters for which the co-annihilationprocesses involving only gauge interactions are sufficient to suppress the relic density belowthe observed value Besides in the left panel the light grey region at large mS andorr corresponds to Yukawa couplings larger than y = 6 which we choose as perturbativitylimit8 Notice that for the most degenerate scenario discussed in this work r = 101 theSommerfeld corrections lead to a change in the relic density of up to 15 It is also worthmentioning that the Sommerfeld effect can both increase as well as decrease the relic densitydepending on the dark matter mass and the mass splitting This is due to the different sign

8Our analysis includes the loop process SS rarr gg that depends on y2g2s16π2 Requiring y2g2

s16π2 1such that the one-loop calculation becomes reliable requires y 6

ndash 7 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

S

q

S

q

ψ

S

q

S

q

ψ

S

q

S

q

q

ψ

g g

S

ψ

S

ψ

ψ

q

g g

S

ψ

S

ψ

q

q

g g

Figure 3 Diagrams contributing to the effective dark matter-nucleon coupling Here q is short foreither u or d Additional diagrams obtained by crossing initial or final states are not shown

of the effective coupling α depending on the initial color state of the annihilation process (cfsection 22)

3 Direct detection constraints

The interaction of dark matter particles with nucleons leads to potentially observable signa-tures in direct detection experiments In the model under study in this paper this interactionis described by the Feynman diagrams shown in figure 3 The diagrams in the upper rowcorrespond to the tree-level scattering off a light quark q being in our case q = u or dthrough the exchange of a fermionic mediator while the one-loop diagrams depicted in thelower row lead to an effective interaction of the dark matter particle with gluons

The effective interaction of S with a light quark q can be cast as the sum of a scalarand a twist-2 contribution [49]

Lq = CqSmqS2qq + CqT (partmicroS)(partνS)Omicroνqtwist-2 (31)

with Omicroνqtwist-2 equivi

2

(qγmicropartνq + qγνpartmicroq minus gmicroν

2q partq

) (32)

By integrating out the mediator ψ in the diagrams shown in the upper row of figure 3 andmatching the result to the effective Lagrangian in eq (31) we obtain

CqS =y2

4m2S

2r2 minus 1

(r2 minus 1)2 CqT =

y2

m4S

1

(r2 minus 1)2 (33)

where q = u (q = d) for dark matter coupling to uR (dR)On the other hand the diagrams in the lower row of figure 3 induce an effective cou-

pling of dark matter to gluons which has been recently discussed in [37] Similarly to thewell-studied simplified model of Majorana dark matter with a colored scalar mediator [50]the scattering amplitude can be decomposed into a short-distance and a long-distance con-tribution This separation is made according to the momentum scale dominating the loop

ndash 8 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

integration the part of the amplitude arising from loop-momenta of the order of the massscale of the heavy particles (ie the dark matter particle or the fermionic mediator) leadsto the short-distance contribution while the part arising from loop-momenta of the order ofthe light quark masses leads to the long-distance contribution The latter involves values ofthe strong coupling constant at a non-perturbatively small momentum scale and hence cannot be reliably calculated in perturbation theory However this contribution is implicitlycontained in the parton distribution function of the light quarks in the nucleon and henceonly the short-distance contribution must be taken into account in the computation of theone-loop diagrams Defining the effective Lagrangian for the dark matter-gluon interaction as

Lg = CgSαSπS2GmicroνGmicroν (34)

the short-distance contribution to CgS reads assuming the limit mq mψ minusmS [37]

CgS =y4

24m2S

1

r2 minus 1 (35)

From the effective Lagrangians to the partons eqs (31) and (34) one can calculatethe effective spin-independent coupling of the dark matter particle S to a nucleon N theresult being [49]

fNmN

= CqSf(N)Tq

+3

4CqTm

2S(q(N)(2) + q(N)(2))minus 8

9CgSf

(N)TG

(36)

where f(N)Tq

f(N)TG

are mass fractions and q(N)(2) q(N)(2) are the second moments of the

parton distribution functions for our numerical analysis we use the values in [37] We showin figure 4 left panel the effective dark matter-proton coupling fpmp expressed in units ofy4m2

S (which is the common pre-factor to each of the terms in eq (36)) as a function ofrminus 1 for the case of dark matter coupling to uR As apparent from the plot the coupling ofdark matter to gluons corresponding to the last term in eq (36) interferes destructively withthe contributions arising from the dark matter scattering off quarks leading to a vanishingdark matter-proton coupling at r 30 A similar behavior is found for fn although thetotal destructive interference occurs at a slightly different mass splitting r 23

Finally from the effective dark matter-nucleon couplings fp and fn one can calculatethe total spin-independent cross section for dark matter scattering off a nucleus with chargeZ and mass number A At zero momentum transfer which is the regime relevant for directdetection experiments it is given by the coherent sum of fp and fn

σA =m2A

π(mS +mA)2[Zfp + (Aminus Z)fn]2 (37)

We find that among all current experiments the LUX experiment [35] gives in most of theparameter space the best limits to the simplified model under scrutiny in this paper9 LUXis based on a xenon target and as is well known has least sensitivity when fnfp minus07the precise value being dependent on the xenon isotope considered In this case commonly

9After this work has been completed the LUX collaboration presented a reanalysis of the 2013 data leadingto improved upper limits on the dark matter scattering cross section [51] However none of our conclusionswould change qualitatively when including the updated limits

ndash 9 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10minus4

10minus3

10minus2

10minus1

1

10

fpmp

y4

m2S

scalar quarkcontribution

twist-2 quarkcontribution

fp for dark matter coupling to uR

10minus2 10minus1 1 10

minus10minus4

minus10minus3

minus10minus2

minus10minus1

-1

minus1050

total fp

gluon contribution

r minus 1

10minus2 10minus1 1 10-2

-1

0

1

2

3

4

50

fnfp for dark matter coupling to uR

fnfp for coupling to uR

fnfp = 0

fnfp = minus07

fnfp

r minus 1

Figure 4 Left panel dark matter-proton coupling fpmp in units of y4m2S for coupling to uR

Right panel ratio of the neutron-to-proton coupling of dark matter also for coupling to uR

referred to as ldquomaximal isospin violationrdquo the total scattering cross section vanishes Weshow in the right panel of figure 4 the ratio fnfp as a function of the mass splitting forthe case of dark matter coupling to uR As follows from the plot in this scenario maximalisospin violation occurs at r 26 for dark matter coupling to uR (this occurs at r 33for dark matter coupling to dR) Hence we fully take into account the actual value of fnfppredicted by the model by defining the effective dark matter-proton cross section σeff

p via

σeffp = σp middot

sumiisinisotopes ξi (Z + (Ai minus Z)fnfp)

2

sumiisinisotopes ξiA

2i

(38)

where ξi is the natural relative abundance of the xenon isotope i In that way σeffp can be

interpreted as the dark matter-proton scattering cross section that under the assumptionof fp = fn would lead to the same number of events in LUX as the actual dark matter-proton cross section σp when taking into account the ratio fnfp predicted by the modelConsequently σeff

p is the quantity that can be compared to the upper limit derived by theLUX collaboration [35] which was derived under the assumption that fp = fn

In figure 5 we show the effective dark matter-proton scattering cross section σeffp in two

different projections of the thermal parameter space In the left panel the color gradientcorresponds to different values of the relative mass difference between the vector-like mediatorand the dark matter particle Let us emphasize that for every dark matter mass and masssplitting we fix the Yukawa coupling y by the requirement of matching the relic abundancecf section 23 As it can be seen from the plot there is a huge scatter in the possible valuesof the scattering cross section over many orders of magnitude Generally speaking for afixed dark matter mass the scattering cross section gets larger for more and more degeneratescenarios ie smaller r due to the resonant enhancement of the dark matter-nucleon couplingfN in the limit r rarr 1 which follows from eqs (33) (35) and (36) However as it can beinferred from figure 2 for a given mass splitting r co-annihilations imply a lower limit onthe dark matter mass from the requirement of matching the observed relic density Hencepoints in the left panel of figure 5 corresponding to a fixed small value of r minus 1 show aturnaround at this dark matter mass which is clearly visible in the plot eg for r = 101(dark blue points) Furthermore we observe that for a given value of mS 200 GeV the

ndash 10 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5 10 102 103 10410minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

5

mS [GeV]

σeff p[cm

2]

Coupling to uR

LUXXENON1Tν floor

001

01

1

10

40

001

01

1

10

40r minus 1

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

10minus2 10minus1 1 10

10minus54

10minus52

10minus50

10minus48

10minus46

10minus44

10minus42

10minus40

10minus38

r minus 1

σeff p[cm

2]

Coupling to uR

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6

1 middot 10minus4

1 middot 10minus3

1 middot 10minus2

01

1

6y

Figure 5 Effective dark matter-proton scattering cross-section σeffp assuming that the thermal

production of S accounts for all of the observed dark matter as a function of the dark matter mass(left panel) and as a function of the ratio between the fermion mediator ψ and the dark matter S(right panel) The color gradient in the left plot corresponds to different values of r = mψmS whilein the right plot to different values of the Yukawa coupling y The solid dashed and dotted lines inthe left plot show respectively the present upper limit on the effective cross section from the LUXexperiment the projected sensitivity of the XENON1T experiment and the neutrino floor calculatedin [52]

effective scattering cross section converges to a fixed value in the limit of r 1 This caneasily be understood by noting that in this limit the most relevant process for the freeze-outof dark matter is the one-loop annihilation of dark matter into gluons scaling as 1r4 whichis precisely the same asymptotic behaviour of the scattering cross section for r 1 as it canbe seen from eqs (33) (35) (36) and (37)

In the left panel of figure 5 we also show the current upper limit from LUX as well asthe projected upper limit for the XENON1T experiment taken from [36] In addition we alsoshow in the plot the ultimate reach of (non-directional) direct detection experiments given bythe scattering cross section corresponding to coherent neutrino scattering in the detector [52]As apparent from the plot for mS 200minus 300 GeV large parts of the parameter space arealready excluded by LUX and for the most degenerate scenarios even dark matter massesaround 2 TeV are already ruled out In the near future XENON1T will continue closingin the region of the parameter space of thermal dark matter in particular for dark massesabove the TeV scale which will be difficult to probe at the LHC (see the discussion in thenext section)

Finally in the right panel of figure 5 we show the effective dark matter-proton scatteringcross section as a function of rminus1 with the color coding corresponding to the Yukawa couplingy and fixing the dark matter mass by the relic density requirement In this projection of theparameter space the suppression of the effective cross section at r 26 becomes apparentdue to the maximal isospin violation occurring at this value of the mass ratio

4 Constraints from searches at the LHC

The model discussed in this work can be efficiently probed at the LHC through the productionof the fermionic mediator ψ After being produced the mediator decays promptly into thedark matter particle S and a light quark hence the signature of interest consists of (atleast) two jets plus missing transverse ET In the following we first discuss the relevant

ndash 11 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

Mprop g2s

q

q

ψ

ψ

g

g

ψ

ψ

g

g

ψ

ψ

ψ

Mprop y2

u

u

ψ

ψ

S

u

u

ψ

ψ

S

Figure 6 Feynman diagrams of the relevant production modes of mediator pairs in proton-protoncollisions Additional diagrams obtained from crossing or charge conjugation of the initial and finalstate are not shown

contributions to the production cross section of the fermionic mediator ψ and subsequentlywe derive constraints on the model by reinterpreting a recent ATLAS search for multiple jetsplus missing ET

41 Production of mediator pairs

We consider the production of mediator pairs ψψ ψψ and ψψ in proton-proton collisions ata center-of-mass energy

radics = 8 TeV10 The relevant Feynman diagrams shown in figure 6

can be divided into two categories first a ψψ pair can be produced from a qq or gg initialstate by QCD interactions as shown in the upper row of figure 6 Secondly for the case ofdark matter coupling to uR a pair of ψψ ψψ or ψψ can be produced from a uu uu or uuinitial state respectively through the t-channel exchange of the dark matter particle S asshown in the lower row of figure 6 An analogous statement holds for dark matter couplingto dR by exchanging u with d in the initial states The amplitudes corresponding to theQCD induced diagrams are independent of the dark matter mass and the Yukawa couplingy in contrast to the processes arising from the Yukawa interaction

In the model discussed in this work the requirement of correctly reproducing the ob-served dark matter abundance via thermal freeze-out can involve rather large Yukawa cou-plings as can be seen in eg figure 2 On the other hand the strong coupling gs 1therefore the production of mediator pairs can be dominated either by the processes involv-ing the Yukawa coupling or by the strong coupling Furthermore for dark matter coupling touR (dR) the production channel uurarr ψψ (ddrarr ψψ) which is driven solely by the Yukawacoupling can have a larger cross section compared to processes involving a qq or gg pair in

10In addition to the processes pp rarr XX with X = ψ ψ considered here the production of mediatorsthrough the process pp rarr XS provide extra contributions to the multiple jets plus missing ET analysisAssuming y = ythermal we have checked that the total production cross sections satisfy σ(pprarr XS) lt σ(pprarrXX) and that the enhancement in the production cross-section obtained when including σ(pp rarr XS) doesnot affect significantly the limits that are presented in figure 8

ndash 12 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10minus2 10minus1 1 10 10210minus2

10minus1

1

10

102

10301 1 2 4 6

r minus 1

σ[p

b]

σonly QCD

excluded byATLAS n-jet+ET

σ(total)thermal

uu

uu

dd

gg

mψ = 500GeV

ythermal

Figure 7 Total cross section for pprarr ψψψψ ψψ atradics = 8 TeV for mψ = 500 GeV together with

the individual contributions from different initial states For the red curves the Yukawa coupling y isset to the value corresponding to ΩDMh

2 = 012 while the blue dashed curve indicates the productioncross section only from pure QCD processes

the initial state due to the large parton distribution function of the up-quark (down-quark)in the proton In our analysis we calculate the leading-order cross section for the final statesψψψψ ψψ using CalcHEP [53] selecting the cteq6l parton distribution function In orderto include next-to-leading order corrections we parametrize the total cross section as

σfull = K σLO (41)

The K-factor has not been fully calculated for this model consequently we treat K as asource of uncertainty varying it in the range [05 2]11

We show in figure 7 the production cross section for the various initial states for theexemplary choice of dark matter coupling to uR and choosing mψ = 500 GeV as well asK = 1 The red curves were calculated for the value of the Yukawa coupling that leadsto the observed dark matter abundance via thermal freeze-out y = ythermal while the bluedashed curve shows for comparison the predicted cross section when taking into accountonly pure QCD processes in the production of mediator pairs Notice the rise of the totalcross section for large values of the mass ratio that is entirely due to the Yukawa inducedprocesses In particular for mψmS amp 12 the production channel uurarr ψψ dominates dueto the large thermal Yukawa coupling as well as due to the large parton distribution functionof the up-quark in the proton as discussed above From figure 7 it also follows that thecross section for the process uurarr ψψ is lower than the pure QCD cross section in the range11 mψmS 13 This is due to the destructive interference of the QCD and Yukawadriven contributions to the process

42 Constraints derived from the multijet ATLAS analysis

The production of ψ can be detected at the LHC through its decay into a quark and the darkmatter particle S Ignoring the higher-order corrections the event topology always consists

11For comparison the K-factor for tt production which is analogous to the QCD productionof ψψ is 17 [54]

ndash 13 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

of two jets arising from the decay of the two mediators together with missing ET associatedto the dark matter particles (this process was considered in [55] neglecting however theimpact of co-annihilations and higher-order effects in the calculation of the dark matterabundance) On the other hand the radiation of quarks or gluons from the initial final oran intermediate state can lead to additional jets which could also be detected Consideringthese extra jets from higher-order processes is important due to two reasons first if theabsolute mass splitting mψ minusmS is below sim 50minus 100 GeV the jet arising from the decay ofψ is too soft to be detected at ATLAS or CMS In that case the additional emission of oneor more hard jets is necessary for the detection of the event (for an analysis of the constraintsof the model employing monojet searches see [41 55]) Secondly even if the mass splittingof the dark matter particle and the mediator is sufficiently large the signal-to-backgroundratio of the n-jet +ET signal can be larger for n gt 2 compared to n = 2 depending on thecharacteristics of the relevant Standard Model background processes Consequently even ifthe absolute cross section is smaller the constraints derived from the multijet processes canbe more stringent than those obtained from the lowest order two-jet topology

In order to confront our model to available LHC data we make use of the ATLAS searchATLAS-CONF-2013-047 [56] for 2-6 jets plus missing ET at

radics = 8 TeV with a luminosity

of 203 fbminus1 For the search ten different signal regions were defined by the collaborationdiffering mainly by the number of jets and the minimal amount of missing ET The dominantStandard Model processes giving rise to the relevant event topologies are the production ofjets together with a weak gauge boson (which can decay invisibly leading to the missing ETsignature) as well as the production of top quarks The expected size of the backgroundin each signal region has been estimated in [56] employing the commonly used approach ofextrapolating the measured number of events from separate control regions and additionallyvalidating the method by directly using Monte Carlo generators for an estimation of theexpected background rates The ATLAS collaboration found no significant excess in any ofthe signal regions and the corresponding observed (expected) 95 CL upper limits on thenumber of signal events in each signal region which can be found in [56] are denoted asS95

obs (S95exp)

On the other hand for a given signal region i the number of expected signal events canbe cast as

Si = σ middot εi middot L (42)

where σ is the total production cross section for pairs of ψ as discussed in section 41 andL = 203 fbminus1 is the luminosity Moreover the efficiency εi is the probability that a givenevent passes all the selection cuts corresponding to the signal region i This quantity dependson the topology of the involved Feynman diagrams and hence has to be recalculated for agiven model For that purpose we have implemented our model in FeynRules [57] and useMadGraph [58] in order to simulate events for the production of mediator pairs with up to twoadditional jets The partonic events are fed to PYTHIA 6 [59] which simulates the showeringand hadronization process As usual in this context in that step one has to take care ofthe possible double counting in the additional jets which should either be included at thematrix element level in the partonic event or as part of the showering process In order toensure a smooth transition between the two regimes we employ the MLM matching schemeusing the parameters Qcut = mψ4 and SHOWERKT=T We explicitly checked that with thischoice the differential jet distributions are smooth as required for a physical meaningfulmatching scheme

ndash 14 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

Finally in order to apply the cuts corresponding to the ATLAS search we useCheckMATE [60] which also implements a detector simulation Concretely for given val-ues of mS mψ and the corresponding Yukawa coupling y = ythermal(mS mψ) we simulateNev events as described above and for every signal region i CheckMATE determines the num-

ber of events N(i)after cuts passing all the cuts Then the efficiency can be obtained through

εi = N(i)after cutsNev As only a finite number of events can be generated the efficiency ob-

tained in this way is subject to Monte Carlo uncertainties In order to take these into accountin a conservative way we replace Si by the 95 CL lower limit on Si given by Siminus196∆Siwhere ∆Si is the 1σ statistical error on the number of expected signal events12 Then the95 CL upper limit on the production cross section following from the observed (expected)number of events in the signal region i is given by

σ(95)obsi = σ middot

S95obsi

Si minus 196∆Si σ

(95)expi = σ middot

S95expi

Si minus 196∆Si (43)

Depending on the specific point in the parameter space a different signal region providesthe most stringent constraint In order not to bias the final result by making a choice of theoptimal signal region based on an over- or under-fluctuation we choose for a given mS and

mψ the signal region giving rise to the smallest expected upper limit σ(95)expi and then use the

observed upper limit σ(95)obsi in that signal region as our final upper limit on the production

cross section As an example this upper limit is shown in figure 7 for mψ = 500 GeV togetherwith the production cross section predicted by the model

We show in figure 8 our limits in the plane spanned by the dark matter mass andthe mass ratio with the upper (lower) panel corresponding to the scenario of dark mattercoupling to uR (dR) The light blue region enclosed by the solid blue line is excluded by ourreanalysis of the ATLAS data adopting K = 1 in eq (41) the blue dashed line correspondsto K = 05 and the blue dotted line to K = 2 Our results for the case of dark mattercoupling to uR show that the ATLAS data rules out dark matter masses below sim 800 GeVfor r amp 15 upon imposing our perturbativity condition y lt 6 This conclusion furthermoreis rather insensitive to the concrete choice of the K factor The ATLAS constraints for thescenario of coupling to dR are slightly weaker due to the smaller parton distribution functionof the down-quark in the proton compared to the up-quark We also show for completenessthe limits from production of vector-like quarks at the Z resonance at LEPI (yellow dotted)and at LEPII (yellow solid) For the former we imposed mψ amp mZ2 For the latterwe assumed that the constraints are essentially kinematical and amount to mψ amp 100 GeVsimilar to LEPII results on squarks searches [61] Besides we also include in the plots as alight red region enclosed by a solid red line the limits from the LUX experiment discussedin section 3 The complementarity of these two different search strategies in probing theparameter space of the model is manifest from the figure collider experiments currentlyprovide the best limits for r amp 14 while direct detection experiments for smaller masssplittings In particular the null results from the ATLAS experiment rules out the region ofldquomaximal isospin violationrdquo at r 26 for a DM coupling to uR (r 30 for a DM coupling todR) for which the sensitivity of xenon-based direct detection experiments is the lowest Wealso show as a dashed red line the projected reach of the upcoming XENON1T experimentwhich will probe dark matter masses in the TeV range for small values of r A future 100 TeVproton-proton collider would perfectly complement the search for large r and in combination

12We generate up to 5middot106 events per point in the parameter space in order to ensure that ∆SiSi 01minus02

ndash 15 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10 102 103 104001

01

1

10

5

mS [GeV]

rminus1

Coupling to uR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

10 102 103 104001

01

1

10

5

mS [GeV]

rminus

1

Coupling to dR

no thermal relic

ytherm

al gt6

LUXXENON-1T

ATLASFermi

LEP I ampII

Figure 8 Summary of constraints from direct and indirect detection and from collider searchesprojected on the mS minus r plane of possible DM candidates (see text for details) Here mS denotesthe mass of the real scalar dark matter candidate S and r = mψmS parametrizes the mass splittingbetween the vector-like fermionic mediator ψ and S

with XENON1T should be able to close in on the parameter space of the model for darkmatter masses as heavy as a few tens of TeV

5 Indirect detection constraints

Indirect dark matter searches using in particular gamma-rays and antiprotons as messengersprovide a complementary avenue to probe our model

ndash 16 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

The model under consideration produces gamma-ray signals in the form of sharp spectralfeatures or in the form of a continuum The sharp spectral features arise mainly from theannihilation final states uuγ and γγ (the contribution to the total spectrum from γZ isa factor tan2 θW 030 smaller and will be neglected here) The photon multiplicitiesare analogous to those produced when the dark matter couples to a lepton which werediscussed in [23 24 26 27] The final state uuγ gives the dominant contribution to theenergy spectrum when the scalar DM and the fermion mediator are very close in masswhile γγ is more important in the opposite case for intermediate regimes the spectrum willbe a linear combination of these two weighted by the corresponding branching fractionsTherefore for a given dark matter mass the observational upper limits on uuγ and γγbracket the upper limit on σuuγ + 2σγγ for any value of the fermion mediator mass Thetotal annihilation section into sharp gamma-ray spectral features σuuγ + 2σγγ is shown infigure 10 left panel in the parameter space spanned by mS and rminus1 = mψmSminus1 togetherwith the band bracketing the excluded values for this quantity The band is bounded by thelimits on σuuγ which were derived in ref [38] employing Fermi-LAT data in the energy range 5- 300 GeV [62] and HESS data in the energy range 500 GeV - 25 TeV [63] as well as by thelimits on 2σγγ derived by the Fermi-LAT collaboration in [62] in the energy range 200 MeV- 500 GeV and by the HESS collaboration in [63] in the energy range 500 GeV - 25 TeVIn the plot it is assumed an Einasto profile [64ndash66] with α = 017 and rs = 20 kpc [64]It follows from figure 10 that the present Fermi-LAT limits on sharp gamma-ray spectralfeatures probe the thermal parameter space of the model for dark matter masses smallerthan a few tens of GeV Here for simplicity we only show the case of dark matter coupling touR for coupling to dR the cross sections predicted by the model are smaller by a factor of afew due to the smaller charge of the d-quark compared to the u-quark leading qualitativelyto a similar conclusion

On the other hand the continuum of gamma-rays is mainly produced by the finalstates uug and gg (we neglect in our analysis the contributions from uuγ and γZ) Similarlyto the discussion above for small mass ratios the energy spectrum of continuum photonsis dominated by annihilations into uug while for large mass ratios by annihilations intogg the corresponding spectra from annihilation in these two extreme cases are shown infigure 913 Again for intermediate regimes the photon spectrum is a combination of thesetwo and therefore one can bracket the upper limit on the cross section for any mediatormass by considering the upper limits on the channels uug and gg The total annihilationcross section for these two processes σuug + σgg is shown in figure 10 right panel togetherwith the band bracketing the upper limits on σuug + σgg from the Fermi-LAT observationsof dSphs [68] and which is bounded by the upper limits on σuug and σgg

14 As can be seenfrom the figure the Fermi-LAT limits on continuum gamma-ray emission from dSphs putconstraints on the parameter space of the model for mS 150 GeV

The annihilation channels uug and gg also produce an antiproton flux which is currentlyconstrained by the PAMELA data [70] (preliminary data from AMS-02 have been presented

13We also show in the same figure the gamma-ray spectrum from the uu final state The VIB differentialcross section is peaked toward Eg sim Euu sim mS at the parton level This explains why the spectrum ingamma-rays and anti-protons is roughly half-way between that from gg and uu in figures 9 (see also ref [67])This is illustrated for a compressed mass spectrum (r = 101) but we have checked that this feature also holdsfor larger values of r

14The Fermi-LAT collaboration has not published limits on these two final states therefore we estimatethese limits following the methodology pursued in [32] using the 95 CL exclusion limits on DM annihilationinto qq from [68] Concretely we use the fact that the total gamma-ray flux eg for the uu channel isproportional to σvuuN

uuγ where Nuu

γ is the number of gamma rays per annihilation within the energy rangeof Fermi-LAT 05 GeVlt Eγ lt 500 GeV We then rescale the Fermi-LAT limits on σvuu to get σvgguug =

ndash 17 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

10minus4 10minus3 10minus2 10minus1 110minus1

1

10

x = EγmS

dNγd

logx

Comparison of gamma ray spectra

mS = 100 GeVr = 101

gg

uu

uug

10minus4 10minus3 10minus2 10minus1 110minus2

10minus1

1

x = KpmS

dNpd

logx

Comparison of antiproton spectra

mS = 100 GeVr = 101

gg

uu

uug

Figure 9 Gamma-ray spectrum (left panel) and antiproton spectrum (right panel) produced bythe dark matter annihilation into gg (dotted black line) and uug (solid blue line) assuming forconcreteness mS = 100 GeV and r = 101 The figure also shows for comparison the correspondingspectra for the final state uu (dotted-dashed red line)

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

2σv γγ+σv uuγ[cm

3s]

Coupling to uR

Fermi uuγ ([38])Fermi γγ ([62])HESS uuγ ([38])HESS γγ ([63])

001

01

1

10

40

001

01

1

10

40r minus 1

10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5 10 102 103 10410minus30

10minus29

10minus28

10minus27

10minus26

10minus25

5

mS [GeV]

σv gg+σv uug[cm

3s]

Coupling to uR

Fermi uug ([68])Fermi gg ([68])PAMELA uug ([72])PAMELA uug ([31])PAMELA gg ([33])

001

01

1

10

40

001

01

1

10

40r minus 1

Figure 10 Cross section σvuuγ + 2σvγγ (left panel) and σvuug + σvgg (right panel) expected forthermally produced dark matter as a function of the dark matter mass the color code indicatesdifferent values of r The left panel also shows the upper limits on σvuuγ and 2σvγγ from the non-observation of sharp spectral features in the Fermi-LAT and HESS data while the right panelthe limits on σvuug and σvgg from the non-observation by the Fermi-LAT of a gamma-ray flux fromdSphs as well as from the non-observation by the PAMELA experiment of an antiproton excess

in [71]) We show in figure 10 right panel the band bracketing the upper limit on σuug +σggusing the limits on σuug derived in [31 72] and the limits on σgg derived in [33] It followsfrom the figure that the antiprotons may probe thermal candidates with a mass up to sim100 GeV it should be borne in mind though that the antiproton limits are rather sensitiveto uncertainties related to cosmic-ray propagation (these uncertainty may be reduced whenmore cosmic ray data will be released by the AMS-02 collaboration)

Finally we confront in figure 8 the limits from indirect detection with those from othersearch strategies on the thermal dark matter parameter space of the model For the sake ofclarity and to avoid cluttering of lines in the figure we only show the limits from dSphs whichare the strongest and the most robust among the indirect detection constraints analyzed inthis paper As apparent from the figure these limits are complementary to those from

σvuuNuuγ Ngguug

γ where we have determined the number of gamma-rays Nuugguugγ using PYTHIA 81 [69]

ndash 18 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

direct detection and colliders and confirm using a completely different search strategy theexclusion of dark matter particles with mass mS 150 GeV and mψmS amp 14

6 Conclusion

In this paper we have studied a simplified dark matter scenario in which a real scalar darkmatter candidate S couples to light standard model quarks through a Yukawa interactioninvolving a new vector-like fermion mediator ψ In order to compute the relic dark matterabundance via thermal freeze-out we have taken into account annihilation into three bodyfinal states involving internal Bremsstrahlung as well as loop processes We have also ac-counted for Sommerfeld corrections of the co-annihilation processes The latter give rise upto a 15 change in the relic density (enhancing or decreasing the one calculated at perturba-tive level) In addition a distinctive feature of our dark matter scenario is that annihilationsinto gg and qqg can be the dominant contributions to the dark matter annihilations both inthe early universe and today

We have investigated three complementary roads in order to test our dark matter sce-narios direct detection dark matter searches collider searches and indirect detection throughannihilation into antiprotons and gamma rays Current constraints from the LUX experi-ment exclude most of the viable parameter space below masses of a hundreds of GeV (as wellas a small island in the TeV range) The reach of the future XENON1T experiment extendsto 10 TeV for low values of mψmSminus1 In addition we have analyzed how the production ofthe fermionic mediator at colliders could complement such constraints To this end we madeuse of an ATLAS search for 2-6 jets + missing ET using pp collision data at

radics = 8 TeV with

L = 203 fb In order to compute the efficiencies corresponding to our particle physics modelwe have simulated events for the production of mediator pairs using Madgraph and appliedthe cuts corresponding to the ATLAS search using CheckMATE Our results are the followingfor masses between sim 30 (100) GeV and 1 TeV such collider searches allow us to probe viabledark matter scenarios that are beyond the reach of current (future) direct detection searchesCombining the multijet + missing ET ATLAS search limit with LUX constraints real scalardark matter coupling to u or d quarks is excluded for masses in the range 5 minus 300 GeVMoreover the ATLAS limit extends up to mS sim 1 TeV for mψmS minus 1 sim O(1) Finallywe have also estimated the limits from indirect detection experiments using gamma-rays andantiprotons as messengers We have found that the most stringent limits on the model stemfrom the non-observation of a gamma-ray flux correlated to the direction of dSphs Theselimits are complementary to those from direct detection and collider experiments and excludethe region mψmS amp 14 mS 150 GeV

Acknowledgments

We would like to thank K Mawatari K De Causmaecker and M Vereecken for helpfuldiscussions on collider constraints and the use of MadGraph and F Maltoni for interestingcomments LLH was supported in part by FWO-Vlaanderen with the post doctoral fellowshipproject 1271513 and the project G020714N by the Belgian Federal Science Policy Officethrough the Interuniversity Attraction Pole P737 and by the Vrije Universiteit Brusselthrough the Strategic Research Program ldquoHigh-Energy Physicsrdquo The work of FG andMT is supported by the Belgian Federal Science Policy Office through the InteruniversityAttraction Pole P737 The work of AI and SW has been partially supported by the DFGcluster of excellence ldquoOrigin and Structure of the Universerdquo the TUM Graduate School andthe Studienstiftung des Deutschen Volkes

ndash 19 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

References

[1] V Silveira and A Zee Scalar phantoms Phys Lett B 161 (1985) 136 [INSPIRE]

[2] J McDonald Gauge singlet scalars as cold dark matter Phys Rev D 50 (1994) 3637[hep-ph0702143] [INSPIRE]

[3] CP Burgess M Pospelov and T ter Veldhuis The minimal model of nonbaryonic darkmatter a singlet scalar Nucl Phys B 619 (2001) 709 [hep-ph0011335] [INSPIRE]

[4] B Patt and F Wilczek Higgs-field portal into hidden sectors hep-ph0605188 [INSPIRE]

[5] M Kadastik K Kannike and M Raidal Matter parity as the origin of scalar dark matterPhys Rev D 81 (2010) 015002 [arXiv09032475] [INSPIRE]

[6] M Frigerio and T Hambye Dark matter stability and unification without supersymmetryPhys Rev D 81 (2010) 075002 [arXiv09121545] [INSPIRE]

[7] C Arbelaez R Longas D Restrepo and O Zapata Fermion dark matter from SO(10) PhysRev D 93 (2016) 013012 [arXiv150906313] [INSPIRE]

[8] W Rodejohann and CE Yaguna Scalar dark matter in the B-L model JCAP 12 (2015) 032[arXiv150904036] [INSPIRE]

[9] N Nagata KA Olive and J Zheng Weakly-interacting massive particles innon-supersymmetric SO(10) grand unified models JHEP 10 (2015) 193 [arXiv150900809][INSPIRE]

[10] Y Mambrini N Nagata KA Olive J Quevillon and J Zheng Dark matter and gaugecoupling unification in nonsupersymmetric SO(10) grand unified models Phys Rev D 91(2015) 095010 [arXiv150206929] [INSPIRE]

[11] J Heeck and S Patra Minimal left-right symmetric dark matter Phys Rev Lett 115 (2015)121804 [arXiv150701584] [INSPIRE]

[12] A Goudelis Y Mambrini and C Yaguna Antimatter signals of singlet scalar dark matterJCAP 12 (2009) 008 [arXiv09092799] [INSPIRE]

[13] CE Yaguna Gamma rays from the annihilation of singlet scalar dark matter JCAP 03(2009) 003 [arXiv08104267] [INSPIRE]

[14] M Gonderinger Y Li H Patel and MJ Ramsey-Musolf Vacuum stability perturbativity andscalar singlet dark matter JHEP 01 (2010) 053 [arXiv09103167] [INSPIRE]

[15] S Profumo L Ubaldi and C Wainwright Singlet scalar dark matter monochromatic γ raysand metastable vacua Phys Rev D 82 (2010) 123514 [arXiv10095377] [INSPIRE]

[16] A Djouadi O Lebedev Y Mambrini and J Quevillon Implications of LHC searches forHiggs-portal dark matter Phys Lett B 709 (2012) 65 [arXiv11123299] [INSPIRE]

[17] JM Cline K Kainulainen P Scott and C Weniger Update on scalar singlet dark matterPhys Rev D 88 (2013) 055025 [arXiv13064710] [INSPIRE]

[18] M Duerr P Fileviez Perez and J Smirnov Scalar dark matter direct vs indirect detectionarXiv150904282 [INSPIRE]

[19] G Bertone CB Jackson G Shaughnessy TMP Tait and A Vallinotto The WIMP forestindirect detection of a chiral square Phys Rev D 80 (2009) 023512 [arXiv09041442][INSPIRE]

[20] C Boehm and P Fayet Scalar dark matter candidates Nucl Phys B 683 (2004) 219[hep-ph0305261] [INSPIRE]

[21] DA Vasquez C Boehm and J Idarraga Signature of sub GeV dark matter particles at LHCand Tevatron Phys Rev D 83 (2011) 115017 [arXiv09125373] [INSPIRE]

ndash 20 ndash

JCAP02(2016)002

[22] P Fileviez Perez and MB Wise Baryon asymmetry and dark matter through the vector-likeportal JHEP 05 (2013) 094 [arXiv13031452] [INSPIRE]

[23] T Toma Internal Bremsstrahlung signature of real scalar dark matter and consistency withthermal relic density Phys Rev Lett 111 (2013) 091301 [arXiv13076181] [INSPIRE]

[24] F Giacchino L Lopez-Honorez and MHG Tytgat Scalar dark matter models with significantinternal Bremsstrahlung JCAP 10 (2013) 025 [arXiv13076480] [INSPIRE]

[25] S Chang R Edezhath J Hutchinson and M Luty Leptophilic effective WIMPs Phys Rev D90 (2014) 015011 [arXiv14027358] [INSPIRE]

[26] A Ibarra T Toma M Totzauer and S Wild Sharp γ-ray spectral features from scalar darkmatter annihilations Phys Rev D 90 (2014) 043526 [arXiv14056917] [INSPIRE]

[27] F Giacchino L Lopez-Honorez and MHG Tytgat Bremsstrahlung and γ ray lines in 3scenarios of dark matter annihilation JCAP 08 (2014) 046 [arXiv14056921] [INSPIRE]

[28] L Bergstrom Radiative processes in dark matter photino annihilation Phys Lett B 225(1989) 372 [INSPIRE]

[29] R Flores KA Olive and S Rudaz Radiative processes in Lsp annihilation Phys Lett B 232(1989) 377 [INSPIRE]

[30] T Bringmann L Bergstrom and J Edsjo New gamma-ray contributions to supersymmetricdark matter annihilation JHEP 01 (2008) 049 [arXiv07103169] [INSPIRE]

[31] M Garny A Ibarra and S Vogl Dark matter annihilations into two light fermions and onegauge boson General analysis and antiproton constraints JCAP 04 (2012) 033[arXiv11125155] [INSPIRE]

[32] T Bringmann X Huang A Ibarra S Vogl and C Weniger Fermi LAT search for internalBremsstrahlung signatures from dark matter annihilation JCAP 07 (2012) 054[arXiv12031312] [INSPIRE]

[33] X Chu T Hambye T Scarna and MHG Tytgat What if dark matter γ-ray lines come withgluon lines Phys Rev D 86 (2012) 083521 [arXiv12062279] [INSPIRE]

[34] M Garny A Ibarra S Rydbeck and S Vogl Majorana dark matter with a coloured mediatorcollider vs direct and indirect searches JHEP 06 (2014) 169 [arXiv14034634] [INSPIRE]

[35] LUX collaboration DS Akerib et al First results from the LUX dark matter experiment atthe Sanford Underground Research Facility Phys Rev Lett 112 (2014) 091303[arXiv13108214] [INSPIRE]

[36] XENON1T collaboration E Aprile The XENON1T dark matter search experiment SpringerProc Phys 148 (2013) 93 [arXiv12066288] [INSPIRE]

[37] J Hisano R Nagai and N Nagata Effective theories for dark matter nucleon scattering JHEP05 (2015) 037 [arXiv150202244] [INSPIRE]

[38] M Garny A Ibarra M Pato and S Vogl Internal bremsstrahlung signatures in light of directdark matter searches JCAP 12 (2013) 046 [arXiv13066342] [INSPIRE]

[39] A Ibarra M Totzauer and S Wild Higher order dark matter annihilations in the Sun andimplications for IceCube JCAP 04 (2014) 012 [arXiv14024375] [INSPIRE]

[40] J Kopp L Michaels and J Smirnov Loopy constraints on leptophilic dark matter and internalBremsstrahlung JCAP 04 (2014) 022 [arXiv14016457] [INSPIRE]

[41] M Papucci A Vichi and KM Zurek Monojet versus the rest of the world I t-channel modelsJHEP 11 (2014) 024 [arXiv14022285] [INSPIRE]

[42] A Ibarra A Pierce NR Shah and S Vogl Anatomy of coannihilation with a scalar toppartner Phys Rev D 91 (2015) 095018 [arXiv150103164] [INSPIRE]

ndash 21 ndash

JCAP02(2016)002

[43] M Garny A Ibarra and S Vogl Signatures of Majorana dark matter with t-channel mediatorsInt J Mod Phys D 24 (2015) 1530019 [arXiv150301500] [INSPIRE]

[44] G Belanger F Boudjema A Pukhov and A Semenov MicrOMEGAs41 two dark mattercandidates Comput Phys Commun 192 (2015) 322 [arXiv14076129] [INSPIRE]

[45] K Griest and D Seckel Three exceptions in the calculation of relic abundances Phys Rev D43 (1991) 3191 [INSPIRE]

[46] A De Simone GF Giudice and A Strumia Benchmarks for dark matter searches at the LHCJHEP 06 (2014) 081 [arXiv14026287] [INSPIRE]

[47] S Cassel Sommerfeld factor for arbitrary partial wave processes J Phys G 37 (2010) 105009[arXiv09035307] [INSPIRE]

[48] R Iengo Sommerfeld enhancement general results from field theory diagrams JHEP 05(2009) 024 [arXiv09020688] [INSPIRE]

[49] M Drees and M Nojiri Neutralino-nucleon scattering revisited Phys Rev D 48 (1993) 3483[hep-ph9307208] [INSPIRE]

[50] J Hisano K Ishiwata and N Nagata Gluon contribution to the dark matter direct detectionPhys Rev D 82 (2010) 115007 [arXiv10072601] [INSPIRE]

[51] LUX collaboration DS Akerib et al Improved WIMP scattering limits from the LUXexperiment arXiv151203506 [INSPIRE]

[52] J Billard L Strigari and E Figueroa-Feliciano Implication of neutrino backgrounds on thereach of next generation dark matter direct detection experiments Phys Rev D 89 (2014)023524 [arXiv13075458] [INSPIRE]

[53] A Belyaev ND Christensen and A Pukhov CalcHEP 34 for collider physics within andbeyond the Standard Model Comput Phys Commun 184 (2013) 1729 [arXiv12076082][INSPIRE]

[54] N Kidonakis Next-to-next-to-leading soft-gluon corrections for the top quark cross section andtransverse momentum distribution Phys Rev D 82 (2010) 114030 [arXiv10094935][INSPIRE]

[55] S Chang R Edezhath J Hutchinson and M Luty Effective WIMPs Phys Rev D 89 (2014)015011 [arXiv13078120] [INSPIRE]

[56] ATLAS collaboration Search for squarks and gluinos with the ATLAS detector in final stateswith jets and missing transverse momentum and 203 fbminus1 of

radics = 8 TeV proton-proton

collision data arXiv14085857 [INSPIRE]

[57] A Alloul ND Christensen C Degrande C Duhr and B Fuks FeynRules 20 mdash A completetoolbox for tree-level phenomenology Comput Phys Commun 185 (2014) 2250[arXiv13101921] [INSPIRE]

[58] J Alwall et al The automated computation of tree-level and next-to-leading order differentialcross sections and their matching to parton shower simulations JHEP 07 (2014) 079[arXiv14050301] [INSPIRE]

[59] T Sjostrand S Mrenna and PZ Skands PYTHIA 64 physics and manual JHEP 05 (2006)026 [hep-ph0603175] [INSPIRE]

[60] M Drees H Dreiner D Schmeier J Tattersall and JS Kim CheckMATE confronting yourfavourite new physics model with LHC data Comput Phys Commun 187 (2014) 227[arXiv13122591] [INSPIRE]

[61] OPAL collaboration G Abbiendi et al Search for scalar top and scalar bottom quarks at LEPPhys Lett B 545 (2002) 272 [Erratum ibid B 548 (2002) 258] [hep-ex0209026] [INSPIRE]

ndash 22 ndash

JCAP02(2016)002

[62] Fermi-LAT collaboration M Ackermann et al Updated search for spectral lines fromGalactic dark matter interactions with pass 8 data from the Fermi Large Area Telescope PhysRev D 91 (2015) 122002 [arXiv150600013] [INSPIRE]

[63] HESS collaboration A Abramowski et al Search for photon-linelike signatures from darkmatter annihilations with HESS Phys Rev Lett 110 (2013) 041301 [arXiv13011173][INSPIRE]

[64] JF Navarro et al The Inner structure of Lambda-CDM halos 3 universality and asymptoticslopes Mon Not Roy Astron Soc 349 (2004) 1039 [astro-ph0311231] [INSPIRE]

[65] AW Graham D Merritt B Moore J Diemand and B Terzic Empirical models for darkmatter halos I Nonparametric construction of density profiles and comparison with parametricmodels Astron J 132 (2006) 2685 [astro-ph0509417] [INSPIRE]

[66] JF Navarro et al The diversity and similarity of cold dark matter halos Mon Not RoyAstron Soc 402 (2010) 21 [arXiv08101522] [INSPIRE]

[67] T Bringmann AJ Galea and P Walia Leading QCD corrections for indirect dark mattersearches a fresh look arXiv151002473 [INSPIRE]

[68] Fermi-LAT collaboration M Ackermann et al Searching for dark matter annihilation fromMilky Way dwarf spheroidal galaxies with six years of Fermi Large Area Telescope data PhysRev Lett 115 (2015) 231301 [arXiv150302641] [INSPIRE]

[69] T Sjostrand S Mrenna and PZ Skands A brief introduction to PYTHIA 81 Comput PhysCommun 178 (2008) 852 [arXiv07103820] [INSPIRE]

[70] O Adriani et al Measurement of the flux of primary cosmic ray antiprotons with energies of60 MeV to 350 GeV in the PAMELA experiment JETP Lett 96 (2013) 621 [INSPIRE]

[71] A Kounine Latest AMS Results The Positron Fraction and the p-barp ratio talk presentedat the AMS Days at CERN April 15ndash17 Geneva Switzerland (2015)

[72] M Asano T Bringmann and C Weniger Indirect dark matter searches as a probe ofdegenerate particle spectra Phys Lett B 709 (2012) 128 [arXiv11125158] [INSPIRE]

ndash 23 ndash