Research Article Constraints to Dark Matter from Inert Higgs ...Research Article Constraints to Dark Matter from Inert Higgs Doublet Model MarcoAurelioDíaz,BenjaminKoch,andSebastiánUrrutia-Quiroga

Research ArticleConstraints to Dark Matter from Inert Higgs Doublet Model

Marco Aurelio Diacuteaz Benjamin Koch and Sebastiaacuten Urrutia-Quiroga

Instituto de Fısica Pontificia Universidad Catolica de Chile Avenida Vicuna Mackenna 4860 Santiago Chile

Correspondence should be addressed to Sebastian Urrutia-Quiroga sgurrutiuccl

Received 19 November 2015 Revised 25 January 2016 Accepted 28 January 2016

Academic Editor Michal Kreps

Copyright copy 2016 Marco Aurelio Dıaz et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited The publication of this article was funded by SCOAP3

We study the Inert Higgs Doublet Model and its inert scalar Higgs119867 as the only source for dark matter It is found that three massregions of the inert scalar Higgs can give the correct dark matter relic density The low mass region (between 3 and 50GeV) isruled out New direct dark matter detection experiments will probe the intermediate (between 60 and 100GeV) and high (heavierthan 550GeV) mass regions Collider experiments are advised to search for119863plusmn rarr 119867119882

plusmn decay in the two jets plus missing energychannel

1 Introduction

Astrophysical observations provide strong evidence for theexistence of dark matter (DM) [1] and its abundance in thecurrent phase of the Universe [2] According to the newestresults fromPlanck collaboration there is 74 approximatelyofmatterwhich is not directly visible but is observed due to itsgravitational effects on visiblematter Additional evidence forthe existence of DM comes from study of the rotation curvesof spiral galaxies [3] the analysis of the bullet cluster [4] andthe study of baryon acoustic oscillations [5] One of the mostcommon hypotheses used to explain these phenomena is topostulate the existence of weakly interactingmassive particles(WIMPs) [6]

In order to explain DM we study a simple extension ofthe Standard Model (SM) called the Inert Higgs DoubletModel (IHDM) This model which was originally proposedfor studies on electroweak (EW) symmetry breaking [7]introduces an additional doublet and a discrete symmetryThese two characteristics of the model modify the SMphenomenology but there are some regions of the parameterspace which predict only small deviations from the SMNevertheless one of the most attractive characteristics of theIHDM is the presence of a stable neutral particle which canbe a DM candidate

In this work the IHDM is revisited considering variousrestrictions focusing our analysis on the zones of the param-eter space which reproduce the correct DM relic density

according to the newest measurements [8 9] In this contextthree not connected mass regimes for the lightest inertparticle are foundThese regimes are also analyzed using LHCobservables like branching ratios to invisible particles anda specific SM-like Higgs boson decay mode Additionallywe study some inert decays modes Finally we use a directdetection approach to rule out one of the mass regimes Itis further shown that this regime can also be ruled out byconstraints from collider physics [10]

This paper is organized as follows After a short intro-duction in Section 1 the model is introduced in Section 2 byformulating the associated potential and constraints of themodel and by exploring the parameter space and its charac-teristics in Section 3 In Section 4 the behavior of the modelis presented from a collider physics perspective studying themodifications of the SM and its implications for the IHDMIn Section 5 the results of this study are complemented byan analysis from the dark matter perspective Finally inSection 6 we remark on the most important conclusions ofour work

2 The Inert Higgs Doublet Model

Consider an extension of Standard Model (SM) whichcontains twoHiggs doubletsΦ

119878119863and a discreteZ

2symmetry

[7] (Φ119878

Z2

997888997888rarr Φ119878and Φ

119863

Z2

997888997888rarr minusΦ119863) All fields of the SM are

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2016 Article ID 8278375 9 pageshttpdxdoiorg10115520168278375

2 Advances in High Energy Physics

invariants under the discrete symmetry andΦ119878is completely

analogous to the SM Higgs doubletThe most general renormalizable 119878119880(2) times 119880(1) invariant

Higgs potential that also preserves the discrete symmetry is

119881 = 1205832

1A + 120583

2

2B + 120582

1A2 + 120582

2B2 + 120582

3AB + 120582

4CdaggerC

+1205825

2(C2 + Cdagger2)

(1)

where A B C are given by

A = Φ119878

daggerΦ119878

B = Φ119863

daggerΦ119863

C = Φ119878

daggerΦ119863

(2)

The parameters 1205832119894(119894 = 1 2) and 120582

119895(119895 = 1 4) are

intrinsically real and 1205825will be assumed to be real [11] After

Spontaneous Symmetry Breaking the vacuum expectationvalues of the Higgs doublets are

⟨Φ119878⟩ =

1

radic2

(

0

V)

⟨Φ119863⟩ = (

0

0)

(3)

where ⟨Φ119863⟩ is forced by the discrete symmetry and V =

246GeV Expanding the fields around those vacua we define

Φ119878= (

119866+

(V + ℎ + 1198941198660)radic2

)

Φ119863= (

119863+

(119867 + 119894119860)

radic2

)

(4)

where 1198660 and 119866plusmn are the neutral and charged Goldstone

bosons and ℎ is the SM-like Higgs boson The fields in thesecond doublet belong to the so-called dark or inert sectorThey are the scalar119867 and pseudoscalar 119860 both neutral andthe charged scalar 119863plusmn As in the SM the parameter 1205832

1is

related to 1205821by the tree-level tadpole condition 1205832

1= minus1205821V2

The masses of physical states [12 13] are

1198982

ℎ= 21205821V2

1198982

119863= 1205832

2+1205823

2V2

1198982

119867= 1198982

119863+ (

1205824+ 1205825

2) V2 = 1205832

2+120582345

2V2

1198982

119860= 1198982

119863+ (

1205824minus 1205825

2) V2

(5)

with

120582345

= 1205823+ 1205824+ 1205825 (6)

As independent and free parameters we take the masses119898119867

119898119860 and 119898

119863at tree-level and the couplings 120582

2and 120582

345

The SM-like Higgs boson mass is fixed now thanks to themeasurement119898

ℎ= 125GeV [14 15]

The constraints we initially impose include vacuum sta-bility at tree-level where constraints on the 120582

119894couplings and

120583119894mass terms appear [16ndash18] perturbation (|120582

119894| lt 8120587) [19 20]

and unitarity [21] where we impose that the scalar potentialis unitary and that several scattering processes between scalarand gauge bosons are bounded electroweak precision teststhrough the 119878119879 and119880 parameters [22] applied to the IHDM[21 23] with 3120590 values given by

119878|119880=0

= 006 plusmn 009

and

119879|119880=0

= 010 plusmn 007

(7)

with a correlation coefficient of +091 [24] and colliderconstraints [16 25ndash27] where we satisfy lower bonds on theHiggs boson masses

The DM particle must be neutral In our analysis weassume it is the 119867 boson thus 119898

119867lt 119898119860and 119898

119867lt 119898119863

which due to (5) translates to

1205824+ 1205825lt 0

and

1205825lt 0

(8)

We do not consider 119860 as the DM candidate because it isanalogous to consider119867 as the DM candidate defining 120582minus

345=

1205823+ 1205824minus 1205825instead of 120582

345

3 IHDM Parameter Space

We randomly scan the parameter space of the IHDM takinginto account all the constraints mentioned in the previoussection Additionally we compute some astrophysical prop-erties of the model using the micrOMEGAs software [28]We consider masses satisfying 1 GeV lt 119898

119894lt 1 TeV where

119894 = 119867119860119863 In addition we consider cosmological mea-surements the DM relic density ΩDMℎ

2 is a property relatedto its abundance in the current phase of the Universe Thisquantity is well measured by WMAP [29] and Planck [30]experiments Following [31] to combine both measurementswe obtain

ΩDMℎ2= 01181 plusmn 00012 (9)

In Figure 1 the coupling 120582345

is shown as a function of theHiggs boson mass119898

119867varying (120583

119894 120582119894119898119860119898119863 and119898

119867) We

work with the hypothesis that the light inert Higgs boson 119867is providing the complete DM density ΩDMℎ

2 given in (9)The color code is as follows red points (dark gray) produce

Advances in High Energy Physics 3

12

10

8

6

4

2

0

minus2

120582345

100 101 102 103

mH (GeV)

Figure 1 Random scan of IHDM parameter space Coupling 120582345

as a function of the DM candidate mass 119898119867 The upper dotted line

is the bound generated by the inert vacuum condition and the lowerdotted line is generated by the vacuum stability condition

a relic density above the 3120590 limit given in (9) blue points(black) produce a relic density within the 3120590 region greenpoints (light gray) produce a relic density below the 3120590 limitRegarding the points that satisfy the relic density we see threeclear regions [12 32] one for low 119898

119867(3 lt 119898

119867lt 50GeV)

another one for medium 119898119867(60 lt 119898

119867lt 100GeV) and

finally one for high values of 119898119867

(119898119867

gt 550GeV) Theexplanation for the gap is related to annihilation processesand it will be given later At 119898

119867lt 3GeV the IHDM can

no longer be compatible with vacuum existence and stability[33 34]

In Figure 2 we have for the same scan and color code themass of the heavy pseudoscalar 119898

119860(a) and the mass of the

charged Higgs 119898119863(b) as a function of the mass of the DM

candidate 119898119867 Due to dedicated pre-LHC collider searches

a bound that captures most of the features is 119898119860gt 100GeV

and 119898119863gt 70GeV This is so with the exception of a small

strip for119898119860lt 100GeV seen in Figure 2(a) where due to the

proximity of the119867 and 119860masses the search loses sensitivityIn this figure the gap in values of 119898

119867when the relic density

is imposed is apparent Notice that the density of solutions islarger when themasses for119867119860 and119863 are close to each otherand that this feature is more pronounced when the masses ofthese particles are near the TeV scale (due to the logarithmicscale) Finally we notice that ΩDMℎ

2 is more sensitive to theparameters 120582

345and 119898

119867(Figure 1) than the masses of the

other inert particles (Figure 2)

4 Collider Physics

As we mentioned before the Higgs boson discovered atCERN in 2012 is the SM-like Higgs boson ℎ of our modelfrom the non-Inert Higgs Doublet field Φ

119878 This particle ℎ

couples to the charged Higgs pair (119863plusmn) which contributesto the diphoton decay width (in this minimal scenario theIHDM cannot account for the reported excess of diphoton

events by ATLAS [35] and CMS [36] collaborations in theirRun-II 13 TeV analyses because the Z

2symmetry prevents

the extra Higgs bosons of the model from decaying into justtwo photons) Γ(ℎ rarr 120574120574) [37] For the same reason 119863plusmn alsocontribute to Γ(ℎ rarr 119885120574)

It is convenient to work with the parameter [21 33 38]

119877120574120574=119861 (ℎ 997888rarr 120574120574)

IHDM

119861 (ℎ 997888rarr 120574120574)SM (10)

The value we use for the SM is Γ(ℎSM rarr 120574120574) = 41MeV [39]ATLAS [40] and CMS [41] collaborations have studied thisdecay mode and if we combined both results [31] we obtain119877exp120574120574

= 114 plusmn 018In Figure 3 we have the parameter 119877

120574120574as a function of

the DM candidate mass 119898119867

(a) and as a function of thecoupling 120582

345(b)The points in parameter space that produce

a correct relic density can be divided into three groups Inthe case of very light masses for the DM candidate (3 lt

119898119867

lt 50GeV approximately) the decay mode ℎ rarr 119867119867

is open and 119877120574120574

is close to zero ruling those masses out[42] In the intermediate mass case approximately between60 and 100GeV there is a region with acceptable solutionscharacterized by 119877

120574120574asymp 1 This region is characterized by

increasingly heavier values for 119860 and 119863plusmn In the large massregion (119898

119867gt 550GeV approximately) the charged Higgs

119863plusmn gives a negligible contribution to the decay ℎ rarr 120574120574 such

that 119877120574120574is close to unity Interestingly Figure 3(b) shows that

perturbative values (|120582345| lt 1) are preferred

In addition if the inert particles are light enough thereare two other two-body decays which are

Γ (ℎ 997888rarr 119867119867) =V2120582345

2

32120587119898ℎ

radic1 minus4119898119867

2

119898ℎ

2

Γ (ℎ 997888rarr 119860119860)

=

(119898119860

2minus 119898119867

2+ 120582345

V22)2

8120587V2119898ℎ


2

119898ℎ

2

(11)

There is no phase space for a two-body decay ℎ rarr 119863plusmn119863∓

It is possible to define the parameter 119877119885120574 in analogy to 119877

120574120574

defined in (10) It is interesting that even though the decayℎ rarr 119885120574 is not well measured it still can give additionalinsight to themodel [43 44] As Figure 4 shows there appearsa very narrow correlation between 119877

120574120574and 119877

119885120574 which is a

common feature for 119877120574120574

versus 119877119885120574

plots [17 18 45] Thebisector branch only contains points that satisfy 119898

119867lt 119898ℎ2

(inert invisible decay channel open) Points of parameterspace which satisfy the relic density and have low DMcandidate mass are ruled out because they produce a verysmall value for 119877

120574120574 By analyzing the characteristics of those

data points one finds that the larger branch includes onlypoints with 119898

119867gt 119898ℎ2 and the ones that also satisfy relic

density are close to 119877120574120574= 119877119885120574

= 1 as was mentioned beforeThe two branches seen in the 119877

120574120574versus 119877

119885120574relation also

appear in the nonnormalized 119861(ℎ rarr 120574120574) versus 119861(ℎ rarr 119885120574)

relation (not shown) But it is reduced only to the long (green)


mH (GeV)

mA

(GeV

)

100 101 102 103101

102

103

(a)

mH (GeV)

mD

(GeV

)

100 101 102 103101

102

103

(b)

Figure 2 Inert Higgs masses119898119860(a) and119898

119863(b) as a function of the DM candidate mass119898

119867 for the same random scan of IHDM parameter

space The horizontal dotted line is due to LEP constraints and the diagonal dotted line is due to the119898119867-DM condition

0

05

1

15

2

25

3

SM valueplusmn3120590 on Rexp

120574120574

R120574120574

mH (GeV)100 101 102 103

(a)

0 2 4 6 8 10 120

05

1

15

2

25

3


120574120574

R120574120574

minus2

120582345

(b)

Figure 3 119877120574120574

parameter as a function of the DM candidate mass 119898119867(a) and the 120582

345coupling (b) for the same random scan of IHDM

parameter space

branch in the Γ(ℎ rarr 120574120574) versus Γ(ℎ rarr 119885120574) relation Furtherone sees that when the ℎ rarr 119867119867 decay channel is closed the119863plusmn loop transforms into the long branch the otherwise SM

dot (the intersection point between the two branches) If theℎ rarr 119867119867 decay channel is open the second branch appearsbecause the ℎ rarr 119867119867 channel tends to dominate [46]

We are also interested in the invisible decay of the SM-likeHiggs boson If the DM candidate mass satisfies119898

119867lt 119898ℎ2

the two-body decay channel ℎ rarr 119867119867 is open which isinvisible for the LHC detectors and shows only as missingmomentum There are measurements for the invisible decayof the SM-like Higgs from the LHC experiments Taking a

simple average of the upper bounds to the invisible decay ratefrom ATLAS [47] and CMS [48] gives 119861(ℎ rarr inv) lt 043 forthe SM-like Higgs boson In Figure 5 we show the branchingratio for the invisible decay of the SM-likeHiggs boson119861(ℎ rarr119867119867) as a function of the mass of the DM candidate 119898

119867

(a) and as a function of the parameter 119877120574120574

(b) In (a) wealso have a horizontal line that shows the upper bound for119861(ℎ rarr 119867119867) mentioned above The threshold 2119898

119867= 119898ℎ

appears clearly in (a) Most of the points with correct relicdensity satisfying 119898

119867lt 60GeV are ruled out because they

produce a very large invisible branching ratio for ℎ On thecontrary most of the points with higher DM candidate mass


0 05 1 15 20

05

1

15

2

25

3


120574120574

R120574120574

RZ120574

Figure 4 Relation between 119877120574120574and 119877

119885120574for the same random scan

of IHDM parameter space

are fine because they produce an invisible branching ratioequal to zero In (b) wherewehave as dashed lines the boundsfromLHC experiments we see a very strong relation between119861(ℎ rarr 119867119867) and119877

120574120574The points that satisfy relic density with

a lowmass for theDMcandidate are simultaneously excludedfrom 119861(ℎ rarr 119867119867) and from 119877

120574120574 The rest of the points satisfy

the boundsTo finalize this section we discuss the branching ratios

for the two observable inert Higgs bosons 119860 and 119863plusmn In

Figure 6 we have the branching ratios for the pseudoscalarHiggs boson (a) as a function of its mass and the branchingratios for the charged Higgs boson (b) as a function of itsmass In (a) we show the decays of the inert pseudoscalarHiggs 119860 which are 119860 rarr 119867119885 (solid line) and 119860 rarr 119863

plusmn119882∓

(dashed line) As can be seen from the Feynman rules theonly unknown parameters the branching ratios depend onare the masses 119898

119867 119898119860 and 119898

119863 Therefore four scenarios

are considered (i) (119898119867 119898119863) = (60 70) (ii) (450 500) (iii)

(50 600) and (iv) (500 800)GeV The gauge boson can beoff shell although we consider the inert Higgs bosons alwayson shell The oscillation near the threshold is due to differentincreasing rates for the decay rates when the gauge boson isoff shell The branching ratio 119861(119860 rarr 119867119885) is always large(because 119898

119867lt 119898119863) while 119861(119860 rarr 119863

plusmn119882∓) can be low near

thresholds There is a crossing point where 119861(119860 rarr 119867119885) =

119861(119860 rarr 119863plusmn119882∓) In (b) we show the decays of the charged

Higgs119863plusmn Analogous scenarios are considered but replacing119898119863by 119898119860 In solid line we have the branching ratio for the

decay 119863plusmn rarr 119867119882plusmn and in dash we have 119863plusmn rarr 119860119882

plusmn In thecase of 119863plusmn there is no crossing point thus 119861(119863plusmn rarr 119867119882

plusmn)

is always larger than 119861(119863plusmn rarr 119860119882plusmn) We remind the reader

that the presence of a Higgs boson119867 in a final state is seen asmissing momentum at the LHC

5 Cosmology and Dark Matter

The existence of darkmatter seems to be well established now[49] There are several candidates for DM among them arethe previously mentionedWIMPs A good particle candidatefor DM must be neutral and stable (or quasi-stable) TheZ2discrete symmetry in the model studied in this paper

ensures that the lightest of the inert Higgs bosons is stableObservation implies it is either 119867 or 119860 (or in a fine tunedscenario both) In this paper we study the former case Animportant restriction this candidate must satisfy is that itsmass density must agree with experimental observationsWe calculate the relic density of our DM candidate usingmicrOMEGAs software [28] To better understand the resultson the relic density we calculate also the thermal averagedannihilation cross section times the relative velocity ⟨120590V⟩ orannihilation cross section for short

In Figure 7 we plot the 119867 relic density as a function ofthe DM candidate mass 119898

119867(a) and the annihilation cross

section also as a function of the DM candidate mass 119898119867(b)

calculated with [28] For the relic density case we also showas an horizontal dashed line the experimentally measuredvalue for ΩDMℎ

2 as given in (9) The scan shows a largedistribution with differences that can reach more than 10orders of magnitude For this reason most of the points inthe scan are ruled out if one demands that 119867 is actuallythe only WIMP responsible for the observed DM signaturesThere are two mass gaps that divide the mass region in threelow mass (3 lt 119898

119867lt 50GeV approximately) medium

mass (60 lt 119898119867

lt 100GeV approximately) and highmass (550 lt 119898

119867approximately) The origin of these mass

gaps is better understood with the aid of the right frame Inthe right frame of Figure 7 we show the annihilation crosssection as a function of the DM candidate mass 119898

119867 with

vertical lines denoting different thresholds The first gap isnear the threshold 119898

119867asymp 119898ℎ2 where the annihilation

channel 119867119867 rarr ℎ becomes very efficient due to the factthat the SM-like Higgs ℎ is on-shell The second gap startsat the thresholds 119898

119867asymp 119898119882

and 119898119867asymp 119898119885 where 119867119867 rarr

119882119882(119885119885) become available and continues later with thethreshold 119898

119867asymp 119898ℎwhere the channel 119867119867 rarr ℎℎ opens

up The annihilation channel 119867119867 rarr 119905119905 also helps Allthese new annihilation channels make the DM annihilationvery efficient and it is not possible to obtain a relic densityaccording to observations On the other hand for larger119898

119867

it is possible to get a correct relic density if the differencebetween the three inert scalar masses is not so large and 120582

345

remains small enough [50] (see Figure 1)We finally study the direct detection prospects of our

DM candidate We do that through the tree-level spin-independent DM-nucleon interaction cross section [51]which applied to our case

120590SIDM-119873 =

120582345

2

(4120587119898ℎ

4)

119898119873

4119891119873

2

(119898119867+ 119898119873)2 (12)

Here 119898ℎis the mass of the SM-like Higgs boson 119898

119867is

the mass of the DM candidate119898119873is the nucleonmass taken

here to be 119898119873

= 0939GeV as the average of the proton


0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)

Figure 5 Branching ratio for the invisible decay of the SM-like Higgs boson as a function of the DM candidate mass119898119867(a) and as a function

of the parameter 119877120574120574(b) for the same random scan of IHDM parameter space Please note that there is a number of points on the 119898

119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)

Figure 6 Branching ratios for the inert Higgs bosons 119860 (a) and 119863plusmn (b) as a function of their corresponding mass

and neutronmasses 120582345

is the combined coupling defined in(6) and 119891

119873is a form factor that depends on hadronic matrix

elements [52 53]In Figure 8 we show the DM-nucleon cross section as

a function of the DM candidate mass for a correct valueof ΩDMℎ

2 We consider three values for 119891119873 a central value

(0326) from a lattice calculation [54] and extreme values(0260 and 0629) from the MILC collaboration [55] Lowerbounds for past experiments and prospects of measurementsfor future experiments are also shown [56ndash59] Notice thatthe dispersion of points for high119898

119867can be understood from

analogous dispersion seen in Figure 1 and the same situation

occurs with the line-like distribution for light 119898119867 We also

show the coherent neutrino scattering upper limit [60] Thiscurve represents the threshold below which the detectorsensitivity is such that not only can the possibleDMscatteringeffects be observed but also the indistinguishable scatteringeffects are associated with neutrinos Thus this indicates aregion where the neutrino background becomes dominantand little information can be obtained onDMeffects Currentdirect detection of DM excludes all the low DMmass pointsand most of the medium DM mass points Allowed are anarrow region near 60GeV and all the highmass regionNotethat the absence of points in the range of sim100ndash550GeV in


mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)

Figure 7 Relic density for119867 as a function of its mass119898119867(a) and annihilation cross section for119867 also as a function of its mass119898

119867(b) for

the same random scan of IHDM parameter space

Coherentneutrinoscattering

CDMSlite upper limitSuperCDMS upper limitLUX upper limit

Xenon1T expected resolutionLZ expected resolution

mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N

Figure 8 Spin-independent DM-nucleon cross section as a func-tion of the DM candidate mass for points of the IHDM withDM relic density consistent with observation Three scenarios areconsidered with different values for the form factor 119891

119873 Lower

bounds for past experiments and prospects of measurements forfuture experiments are shown

this plot is due to the fact that the plotted points are onlythose that give the right dark matter density (ldquoblue pointsrdquo)Future experiments will be able to test large parts of these tworegions but will not be able to rule them out entirely if thereis no signal

6 Conclusions

In this paper the Inert Higgs Doublet Model is studied withthe inert Higgs boson 119867 as a DM candidate using the latest

results for DM relic density annihilation cross section andcollider searches As a summary we highlight the following

(i) The branching ratios for the charged Higgs 119863plusmn andfor the pseudoscalar Higgs 119860 are studied and shownin Figure 6 The Z

2symmetry strongly reduces the

number of different decay channels Considering theHiggs boson on shell and allowing the gauge boson tobe off shell (a different choice would produce differentdecay channels but with smaller branching ratios)we find that 119861(119863plusmn rarr 119867119882

plusmn) gt 119861(119863

plusmnrarr 119860119882

plusmn) as

opposed to the 119860 decays where there is a crossingpoint not far from the threshold For this reason incollider searches we recommend to look for a signalfor a 119863plusmn two jets (consistent with a119882) and missingenergy (from the DM candidate119867)

(ii) Three distinct 119867 mass regions are found that pro-duced the correct relic density (ie 119867 is the onlysource for DM) as can be seen in Figure 7 The lowmass region (between 3 and 50GeV approximately)is already ruled out because it produces a very smallvalue for 119877

120574120574(Figure 3) because it produces a very

high value for 119861(ℎ rarr 119867119867) (Figure 5) and becauseof direct DM searches (Figure 8) The intermediatemass region (between 60 and 100GeV approximately)and the high mass region (heavier than 550GeVapproximately) are allowed

(iii) In Figure 8 we study the DM candidate direct detec-tion The low mass region is also ruled out by presentexperiments In addition future experiments willprobe intermediate and high mass regions Neverthe-less in absence of signals it will not be possible torule out these two regions Notice the proximity of


the region where the coherent neutrino scattering isan irreducible background

With this one sees that the Inert Higgs Doublet Model gives astill viable DM candidate which will most likely be tested bydirect DM detection experiments

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for conversations with Drs GermanGomez Nicolas Viaux and Edson Carquın Marco Aure-lio Dıaz was partly supported by Fondecyt 1141190 Ben-jamin Koch was partly supported by Fondecyt 1120360Sebastian Urrutia-Quiroga was partly supported by post-graduate CONICYT grantThe work of all of the authors wasalso partly financed byCONICYTGrant ANILLOACT-1102

References

[1] D Clowe M Bradac A H Gonzalez et al ldquoA direct empiricalproof of the existence of darkmatterrdquoTheAstrophysical Journalvol 648 no 2 pp L109ndashL113 2006

[2] P A R Ade N AghanimM I Alves et al ldquoPlanck 2013 resultsI Overview of products and scientific resultsrdquo Astronomy ampAstrophysics vol 571 article A1 2014

[3] V C Rubin W K Ford Jr and N Thonnard ldquoRotationalproperties of 21 SC galaxies with a large range of luminositiesand radii from NGC 4605R = 4 kpc to UGC 2885R =122 kpcrdquo Astrophysical Journal vol 238 pp 471ndash487 1980

[4] M Markevitch A H Gonzalez D Clowe et al ldquoDirectconstraints on the dark matter self-interaction cross-sectionfrom the merging galaxy cluster 1E0657-56rdquo The AstrophysicalJournal vol 606 no 2 pp 819ndash824 2004

[5] W J Percival S Cole D J Eisenstein et al ldquoMeasuring thebaryon acoustic oscillation scale using the sloan digital skysurvey and 2dF galaxy redshift surveyrdquo Monthly Notices of theRoyal Astronomical Society vol 381 no 3 pp 1053ndash1066 2007

[6] C J Copi D N Schramm and M S Turner ldquoBig-bangnucleosynthesis and the baryondensity of the universerdquo Sciencevol 267 no 5195 pp 192ndash199 1995

[7] N G Deshpande and E Ma ldquoPattern of symmetry breakingwith two Higgs doubletsrdquo Physical Review D vol 18 no 7 pp2574ndash2576 1978

[8] N Blinov J Kozaczuk D E Morrissey and A de laPuente ldquoCompressingthe inert doubletmodelrdquo httparxivorgabs151008069

[9] N Khan and S Rakshit ldquoConstraints on inert dark matter fromthe metastability of the electroweak vacuumrdquo Physical ReviewD vol 92 no 5 Article ID 055006 2015

[10] G Belanger B Dumont A Goudelis B Herrmann S Kramland D Sengupta ldquoDilepton constraints in the inert doubletmodel from Run 1 of the LHCrdquo Physical Review D vol 91 no11 Article ID 115011 2015

[11] I F Ginzburg K A Kanishev M Krawczyk and DSokolowska ldquoEvolution of Universe to the present inert phaserdquoPhysical Review D vol 82 Article ID 123533 2010

[12] L LopezHonorez andC E Yaguna ldquoThe inert doubletmodel ofdark matter revisitedrdquo Journal of High Energy Physics vol 2010no 9 article 046 2010

[13] A Arhrib Y L S Tsai Q Yuan and T C Yuan ldquoAn updatedanalysis of Inert Higgs Doublet Model in light of the recentresults from LUX PLANCK AMS-02 and LHCrdquo Journal ofCosmology and Astroparticle Physics vol 2014 no 6 article 302014

[14] G Aad T Abajyan B Abbott et al ldquoObservation of a newparticle in the search for the Standard Model Higgs boson withthe ATLAS detector at the LHCrdquo Physics Letters B vol 716 no1 pp 1ndash29 2012

[15] S Chatrchyan et al ldquoObservation of a new boson with massnear 125 GeV in pp collisions at radic119878 = 7 and 8 TeVrdquo Journal ofHigh Energy Physics vol 2013 article 81 2013

[16] M Gustafsson ldquoThe inert doublet model and its phe-nomenologyrdquo in Proceedings of the Prospects for Charged HiggsConference (PoS CHARGED rsquo10) vol 30 2010 httparxivorgabs11061719

[17] E C F S Fortes A C B Machado J Montano and V PleitezldquoPrediction of ℎ rarr 120574119885 fromℎ rarr 120574120574 at the LHC for the IMDS

3

modelrdquo Journal of Physics G Nuclear and Particle Physics vol42 no 11 Article ID 115001 2015

[18] M Krawczyk D Sokołowska P Swaczyna and B SwiezewskaldquoHiggsrarr 120574120574 Z120574 in the inert doublet modelrdquo Acta PhysicaPolonica B vol 44 no 11 pp 2163ndash2170 2013

[19] R Barbieri L J Hall and V S Rychkov ldquoImproved naturalnesswith a heavy Higgs boson an alternative road to CERN LHCphysicsrdquo Physical Review D vol 74 no 1 Article ID 0150072006

[20] A Djouadi ldquoThe anatomy of electroweak symmetry breakingtome I theHiggs boson in the StandardModelrdquoPhysics Reportsvol 457 no 1ndash4 pp 1ndash216 2008

[21] A Arhrib R Benbrik and N Gaur ldquo119867 rarr 120574120574 in the inertHiggs doublet modelrdquo Physical Review D vol 85 no 9 ArticleID 095021 2012

[22] M E Peskin and T Takeuchi ldquoEstimation of oblique elec-troweak correctionsrdquo Physical Review D vol 46 no 1 pp 381ndash409 1992

[23] B Swiezewska ldquoYukawa independent constraints for two-Higgs-doublet models with a 125GeV Higgs bosonrdquo PhysicalReview D vol 88 no 5 Article ID 055027 2013 ErratumPhysical Review D vol 88 no 11 Article ID 119903 2013

[24] M Baak J Cuth J Haller et al ldquoThe global electroweak fitat NNLO and prospects for the LHC and ILCrdquo The EuropeanPhysical Journal C vol 74 article 3046 pp 1ndash14 2014

[25] E Lundstrom M Gustafsson and J Edsjo ldquoInert doubletmodel and LEP II limitsrdquo Physical Review D vol 79 no 3Article ID 035013 2009

[26] Q H Cao E Ma and G Rajasekaran ldquoObserving the darkscalar doublet and its impact on the standard-model Higgsboson at collidersrdquo Physical Review D vol 76 no 9 Article ID095011 2007

[27] A Pierce and JThaler ldquoNatural DarkMatter from an unnaturalHiggs boson and new colored particles at the TeV scalerdquo Journalof High Energy Physics vol 2007 no 8 article 026 2007

[28] G Belanger F Boudjema and A Pukhov ldquomicrOMEGAs acode for the calculation of Dark Matter properties in genericmodels of particle interactionrdquo httparxivorgabs14020787

[29] C L Bennett D Larson J LWeiland et al ldquoNine-yearWilkin-son Microwave Anisotropy Probe (WMAP) observations final


maps and resultsrdquoThe Astrophysical Journal Supplement Seriesvol 208 no 2 article 20 2013

[30] P A R Ade N Aghanim M Arnaud et al ldquoPlanck 2015results XIIICosmological parametersrdquo httparxivorgabs150201589

[31] G Bohm andG Zech Introduction to Statistics andData Analy-sis for Physicists Deutsches Elektronen-Synchrotron HamburgGermany 2010

[32] L Lopez Honorez and C E Yaguna ldquoA new viable region ofthe inert doubletmodelrdquo Journal of Cosmology andAstroparticlePhysics vol 2011 no 1 article 002 2011

[33] A Goudelis B Herrmann andO Stal ldquoDarkmatter in the inertdoublet model after the discovery of a Higgs-like boson at theLHCrdquo Journal of High Energy Physics vol 2013 article 106 2013

[34] M Cirelli N Fornengo andA Strumia ldquoMinimal darkmatterrdquoNuclear Physics B vol 753 no 1-2 pp 178ndash194 2006

[35] ATLAS Collaboration ldquoSearch for resonances decaying tophoton pairs in 32 fbminus1 of pp collisions at radic119904 = 13 TeV withthe ATLAS detectorrdquo ATLAS-CONF-2015-081

[36] CMS Collaboration ldquoSearch for new physics in high massdiphoton events in proton-proton collisions at radic119904 = 13TeVrdquoCMS-PAS-EXO-15-004 2015

[37] J F GunionH EHaber G L Kane and S Dawson ldquoTheHiggshunterrsquos guiderdquo Frontiers of Physics vol 80 pp 1ndash448 2000

[38] M Krawczyk D Sokolowska P Swaczyna and B SwiezewskaldquoConstraining Inert Dark Matter by R

120574120574and WMAP datardquo

Journal of High Energy Physics vol 2013 article 55 2013[39] A Djouadi J Kalinowski and M Spira ldquoHDECAY a program

for Higgs boson decays in the Standard Model and its super-symmetric extensionrdquo Computer Physics Communications vol108 no 1 pp 56ndash74 1998

[40] G Aad B Abbott J Abdallah et al ldquoMeasurement of Higgsbosonproduction in the diphotondecay channel in pp collisionsat center-of-mass energies of 7 and 8 TeV with the ATLASdetectorrdquo Physical Review D vol 90 no 11 Article ID 1120152014

[41] V Khachatryan A M Sirunyan A Tumasyan et al ldquoPrecisedetermination of the mass of the Higgs boson and tests of com-patibility of its couplings with the standard model predictionsusing proton collisions at 7 and 8TeVrdquo The European PhysicalJournal C vol 75 no 5 article 212 2015

[42] A Ilnicka M Krawczyk and T Robens ldquoThe Inert DoubletModel in thelight of LHC and astrophysical datamdashan updaterdquohttparxivorgabs150801671

[43] G Aad T Abajyan B Abbott et al ldquoSearch for Higgs bosondecays to a photon and a Z boson in pp collisions atradic119878 = 7 and8 TeV with the ATLAS detectorrdquo Physics Letters B vol 732 pp8ndash27 2014

[44] S ChatrchyanVKhachatryanAM Sirunyan et al ldquoSearch fora Higgs boson decaying into a Z and a photon in pp collisionsat radic119904 = 7 and 8 TeVrdquo Physics Letters B vol 726 no 4-5 pp587ndash609 2013

[45] C S Chen C Q Geng D Huang and L H Tsai ldquoNew scalarcontributions to ℎ rarr 119885120574rdquo Physical Review D vol 87 no 7Article ID 075019 2013

[46] B Swiezewska and M Krawczyk ldquoDiphoton rate in the inertdoublet model with a 125GeVHiggs bosonrdquo Physical Review Dvol 88 no 3 Article ID 035019 2013

[47] G Aad B Abbott J Abdallah et al ldquoSearch for invisible decaysof a Higgs boson using vector-boson fusion in pp collisions atradic119878 = 8 TeV with the ATLAS detectorrdquo Journal of High EnergyPhysics vol 2016 article 172 2016

[48] S Chatrchyan V Khachatryan A M Sirunyan et al ldquoSearchfor invisible decays of Higgs bosons in the vector boson fusionand associated ZH production modesrdquo The European PhysicalJournal C vol 74 article 2980 2014

[49] K A Olive K Agashe C Amsler et al ldquoReview of particlephysicsrdquo Chinese Physics C vol 38 no 9 Article ID 0900012014

[50] T Hambye F-S Ling L Lopez Honorez and J Rocher ldquoScalarmultiplet darkmatterrdquo Journal of High Energy Physics vol 2009no 7 article 090 2009 Erratum in Journal of High EnergyPhysics vol 2010 no 5 article 066 2010

[51] A Djouadi O Lebedev Y Mambrini and J Quevillon ldquoImpli-cations of LHC searches for Higgs-portal dark matterrdquo PhysicsLetters B vol 709 no 1-2 pp 65ndash69 2012

[52] S Kanemura SMatsumoto T Nabeshima andNOkada ldquoCanWIMPdarkmatter overcome the nightmare scenariordquo PhysicalReview D vol 82 no 5 Article ID 055026 2010

[53] J M Alarcon L S Geng J Martin Camalich and J A OllerldquoThe strangeness content of the nucleon from effective fieldtheory and phenomenologyrdquoPhysics Letters B vol 730 pp 342ndash346 2014

[54] RD Young andAWThomas ldquoOctet baryonmasses and sigmaterms from an SU(3) chiral extrapolationrdquo Physical Review Dvol 81 Article ID 014503 2010

[55] D Toussaint andW Freeman ldquoStrange quark condensate in thenucleon in 2 + 1 flavor QCDrdquo Physical Review Letters vol 103no 12 Article ID 122002 2009

[56] D S Akerib H M Araujo X Bai et al ldquoFirst results fromthe LUX dark matter experiment at the sanford undergroundresearch facilityrdquo Physical Review Letters vol 112 no 9 ArticleID 091303 2014

[57] R Agnese A J Anderson M Asai et al ldquoSearch for low-mass weakly interactingmassive particles using voltage-assistedcalorimetric ionization detection in the superCDMS experi-mentrdquo Physical Review Letters vol 112 no 4 Article ID 0413022014

[58] R Agnese A J Anderson M Asai et al ldquoSearch for low-mass weakly interacting massive particles with SuperCDMSrdquoPhysical Review Letters vol 112 no 24 Article ID 241302 2014

[59] R Gaitskell M De Jesus and L RoszkowskiDarkMatter ToolsWorkgroup University of California Berkeley Berkeley CalifUSA httpdmtoolsberkeleyedu

[60] J Billard E Figueroa-Feliciano and L Strigari ldquoImplicationof neutrino backgrounds on the reach of next generation darkmatter direct detection experimentsrdquo Physical ReviewD vol 89no 2 Article ID 023524 2014

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


invariants under the discrete symmetry andΦ119878is completely

analogous to the SM Higgs doubletThe most general renormalizable 119878119880(2) times 119880(1) invariant

Higgs potential that also preserves the discrete symmetry is

119881 = 1205832

1A + 120583

2

2B + 120582

1A2 + 120582

2B2 + 120582

3AB + 120582

4CdaggerC

+1205825

2(C2 + Cdagger2)

(1)

where A B C are given by

A = Φ119878

daggerΦ119878

B = Φ119863

daggerΦ119863

C = Φ119878

daggerΦ119863

(2)

The parameters 1205832119894(119894 = 1 2) and 120582

119895(119895 = 1 4) are

intrinsically real and 1205825will be assumed to be real [11] After

Spontaneous Symmetry Breaking the vacuum expectationvalues of the Higgs doublets are

⟨Φ119878⟩ =

1

radic2

(

0

V)

⟨Φ119863⟩ = (

0

0)

(3)

where ⟨Φ119863⟩ is forced by the discrete symmetry and V =

246GeV Expanding the fields around those vacua we define

Φ119878= (

119866+

(V + ℎ + 1198941198660)radic2

)

Φ119863= (

119863+

(119867 + 119894119860)

radic2

)

(4)

where 1198660 and 119866plusmn are the neutral and charged Goldstone

bosons and ℎ is the SM-like Higgs boson The fields in thesecond doublet belong to the so-called dark or inert sectorThey are the scalar119867 and pseudoscalar 119860 both neutral andthe charged scalar 119863plusmn As in the SM the parameter 1205832

1is

related to 1205821by the tree-level tadpole condition 1205832

1= minus1205821V2

The masses of physical states [12 13] are

1198982

ℎ= 21205821V2

1198982

119863= 1205832

2+1205823

2V2

1198982

119867= 1198982

119863+ (

1205824+ 1205825

2) V2 = 1205832

2+120582345

2V2

1198982

119860= 1198982

119863+ (

1205824minus 1205825

2) V2

(5)

with

120582345

= 1205823+ 1205824+ 1205825 (6)

As independent and free parameters we take the masses119898119867

119898119860 and 119898

119863at tree-level and the couplings 120582

2and 120582

345

The SM-like Higgs boson mass is fixed now thanks to themeasurement119898

ℎ= 125GeV [14 15]

The constraints we initially impose include vacuum sta-bility at tree-level where constraints on the 120582

119894couplings and

120583119894mass terms appear [16ndash18] perturbation (|120582

119894| lt 8120587) [19 20]

and unitarity [21] where we impose that the scalar potentialis unitary and that several scattering processes between scalarand gauge bosons are bounded electroweak precision teststhrough the 119878119879 and119880 parameters [22] applied to the IHDM[21 23] with 3120590 values given by

119878|119880=0

= 006 plusmn 009

and

119879|119880=0

= 010 plusmn 007

(7)

with a correlation coefficient of +091 [24] and colliderconstraints [16 25ndash27] where we satisfy lower bonds on theHiggs boson masses

The DM particle must be neutral In our analysis weassume it is the 119867 boson thus 119898

119867lt 119898119860and 119898

119867lt 119898119863

which due to (5) translates to

1205824+ 1205825lt 0

and

1205825lt 0

(8)

We do not consider 119860 as the DM candidate because it isanalogous to consider119867 as the DM candidate defining 120582minus

345=

1205823+ 1205824minus 1205825instead of 120582

345

3 IHDM Parameter Space

We randomly scan the parameter space of the IHDM takinginto account all the constraints mentioned in the previoussection Additionally we compute some astrophysical prop-erties of the model using the micrOMEGAs software [28]We consider masses satisfying 1 GeV lt 119898

119894lt 1 TeV where

119894 = 119867119860119863 In addition we consider cosmological mea-surements the DM relic density ΩDMℎ

2 is a property relatedto its abundance in the current phase of the Universe Thisquantity is well measured by WMAP [29] and Planck [30]experiments Following [31] to combine both measurementswe obtain

ΩDMℎ2= 01181 plusmn 00012 (9)

In Figure 1 the coupling 120582345

is shown as a function of theHiggs boson mass119898

119867varying (120583

119894 120582119894119898119860119898119863 and119898

119867) We

work with the hypothesis that the light inert Higgs boson 119867is providing the complete DM density ΩDMℎ

2 given in (9)The color code is as follows red points (dark gray) produce


12

10

8

6

4

2

0

minus2

120582345

100 101 102 103

mH (GeV)





119867(3 lt 119898

119867lt 50GeV)




(119898119867















345and 119898



4 Collider Physics





2symmetry prevents



119877120574120574=119861 (ℎ 997888rarr 120574120574)

IHDM

119861 (ℎ 997888rarr 120574120574)SM (10)








119898119867


is open and 119877120574120574









Γ (ℎ 997888rarr 119867119867) =V2120582345

2

32120587119898ℎ


2

119898ℎ

2

Γ (ℎ 997888rarr 119860119860)

=

(119898119860

2minus 119898119867

2+ 120582345

V22)2

8120587V2119898ℎ


2

119898ℎ

2

(11)



120574120574


120574120574and 119877

119885120574 which is a


versus 119877119885120574


119867lt 119898ℎ2







120574120574versus 119877





mH (GeV)

mA

(GeV

)

100 101 102 103101

102

103

(a)

mH (GeV)

mD

(GeV

)

100 101 102 103101

102

103

(b)





0

05

1

15

2

25

3


120574120574

R120574120574

mH (GeV)100 101 102 103

(a)

0 2 4 6 8 10 120

05

1

15

2

25

3


120574120574

R120574120574

minus2

120582345

(b)

Figure 3 119877120574120574



parameter space




119867lt 119898ℎ2



119867



119867= 119898ℎ





0 05 1 15 20

05

1

15

2

25

3


120574120574

R120574120574

RZ120574











plusmn119882∓


119867 119898119860 and 119898




119867lt 119898119863) while 119861(119860 rarr 119863







plusmn)












mass (60 lt 119898119867




119867 with




119867asymp 119898119882





119867


345



120590SIDM-119873 =

120582345

2

(4120587119898ℎ

4)

119898119873

4119891119873

2

(119898119867+ 119898119873)2 (12)


119867is


here to be 119898119873



0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)



119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)














mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




12

10

8

6

4

2

0

minus2

120582345

100 101 102 103

mH (GeV)





119867(3 lt 119898

119867lt 50GeV)




(119898119867















345and 119898



4 Collider Physics





2symmetry prevents



119877120574120574=119861 (ℎ 997888rarr 120574120574)

IHDM

119861 (ℎ 997888rarr 120574120574)SM (10)








119898119867


is open and 119877120574120574









Γ (ℎ 997888rarr 119867119867) =V2120582345

2

32120587119898ℎ


2

119898ℎ

2

Γ (ℎ 997888rarr 119860119860)

=

(119898119860

2minus 119898119867

2+ 120582345

V22)2

8120587V2119898ℎ


2

119898ℎ

2

(11)



120574120574


120574120574and 119877

119885120574 which is a


versus 119877119885120574


119867lt 119898ℎ2







120574120574versus 119877





mH (GeV)

mA

(GeV

)

100 101 102 103101

102

103

(a)

mH (GeV)

mD

(GeV

)

100 101 102 103101

102

103

(b)





0

05

1

15

2

25

3


120574120574

R120574120574

mH (GeV)100 101 102 103

(a)

0 2 4 6 8 10 120

05

1

15

2

25

3


120574120574

R120574120574

minus2

120582345

(b)

Figure 3 119877120574120574



parameter space




119867lt 119898ℎ2



119867



119867= 119898ℎ





0 05 1 15 20

05

1

15

2

25

3


120574120574

R120574120574

RZ120574











plusmn119882∓


119867 119898119860 and 119898




119867lt 119898119863) while 119861(119860 rarr 119863







plusmn)












mass (60 lt 119898119867




119867 with




119867asymp 119898119882





119867


345



120590SIDM-119873 =

120582345

2

(4120587119898ℎ

4)

119898119873

4119891119873

2

(119898119867+ 119898119873)2 (12)


119867is


here to be 119898119873



0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)



119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)














mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




mH (GeV)

mA

(GeV

)

100 101 102 103101

102

103

(a)

mH (GeV)

mD

(GeV

)

100 101 102 103101

102

103

(b)





0

05

1

15

2

25

3


120574120574

R120574120574

mH (GeV)100 101 102 103

(a)

0 2 4 6 8 10 120

05

1

15

2

25

3


120574120574

R120574120574

minus2

120582345

(b)

Figure 3 119877120574120574



parameter space




119867lt 119898ℎ2



119867



119867= 119898ℎ





0 05 1 15 20

05

1

15

2

25

3


120574120574

R120574120574

RZ120574











plusmn119882∓


119867 119898119860 and 119898




119867lt 119898119863) while 119861(119860 rarr 119863







plusmn)












mass (60 lt 119898119867




119867 with




119867asymp 119898119882





119867


345



120590SIDM-119873 =

120582345

2

(4120587119898ℎ

4)

119898119873

4119891119873

2

(119898119867+ 119898119873)2 (12)


119867is


here to be 119898119873



0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)



119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)














mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0 05 1 15 20

05

1

15

2

25

3


120574120574

R120574120574

RZ120574











plusmn119882∓


119867 119898119860 and 119898




119867lt 119898119863) while 119861(119860 rarr 119863







plusmn)












mass (60 lt 119898119867




119867 with




119867asymp 119898119882





119867


345



120590SIDM-119873 =

120582345

2

(4120587119898ℎ

4)

119898119873

4119891119873

2

(119898119867+ 119898119873)2 (12)


119867is


here to be 119898119873



0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)



119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)














mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

02

04

06

08

1

mH (GeV)100 101 102 103

B(h

rarrHH)

(a)

0 05 1 15 2 25 30

02

04

06

08

1

B(h

rarrHH)

R120574120574

(b)



119867and

119877120574120574axes with 119861(ℎ rarr 119867119867) = 0

100 300 500 700 900 1100 1300 1500mA (GeV)

100

10minus1

10minus2

10minus3

(mHmD) = (60 70)

(mHmD) = (450 500)

(mHmD) = (50 600)

(mHmD) = (500 800)

B(A

rarrHZD

plusmnW

∓)

ArarrHZ

ArarrDplusmnW∓

(a)

100 300 500 700 900 1100 1300 1500

100

10minus1

10minus2

10minus3

B(D

plusmnrarr

HW

plusmnA

Wplusmn

)

mD (GeV)

(mHmA) = (60 70)

(mHmA) = (450 500)

(mHmA) = (50 600)

(mHmA) = (500 800)

DplusmnrarrHWplusmn

DplusmnrarrAWplusmn

(b)














mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




mH (GeV)100 101 102 103

105

100

10minus5

ΩD

Mh2

(a)

mH (GeV)100 101 102 103

10minus30

10minus22

10minus24

10minus26

10minus28

mH = mb

mH = mh2mH = mW

mH = mh

⟨120590⟩

(cm

3sminus

1)

(b)


119867(b) for





mH (GeV)100 101 102 103

10minus14

10minus2

10minus4

10minus6

10minus8

10minus10

10minus12

120590SI

(pb)

DM

-N


119873 Lower



6 Conclusions






plusmn) gt 119861(119863


plusmn) as











Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








Acknowledgments


References


















3






















































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics











































FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



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