Scalar Dark Matter candidate in Multi-Higgs Modelsmoriond.in2p3.fr/QCD/2017/SundayMorning/Sokolowska.pdf · MotivationI(2+1)HDM mS 1 < mZ LHCConclusion Scalar Dark Matter candidate

Motivation I(2+1)HDM mS1< mZ LHC Conclusion

Scalar Dark Matter candidatein Multi-Higgs Models

Dorota Sokołowska

University of Warsaw, Faculty of Physics,Institute of Theoretical Physics

Moriond QCD, La Thuile, 26.03.2017

based onJHEP 1612 (2016) 014 and work in progress

with A. Cordero-Cid, J. Hernandez-Sanchez, V. Keus,S. F. King, S. Moretti, D. Rojas

1 / 24


The Standard Model

A rigorously tested Theory of Fundamental Interactions

From the LHC:

• a Higgs particle found in 2012

• no significant deviation from the SM

• no sign of New Physics

But no explanation for:

• Dark Matter

• neutrino masses

• baryon asymmetry and baryogenesis

• extra source of CP violation

• vacuum stability

• ...

Parameter value1− 0.5− 0 0.5 1 1.5 2 2.5 3 3.5 4

bbµ

ττµ

WWµ

ZZµ

γγµ

Run 1LHCCMS and ATLAS ATLAS+CMS

ATLAS

CMS

σ1±σ2±

JHEP 08 (2016) 045

2 / 24


Dark MatterEvidence for Dark Matter at diverse scales:

• galaxy scales: rotational speeds of galaxies

• cluster scales: gravitational lensing at galaxy clusters

• horizon scales: anisotropies in the CMB

⇒ around 25 % of the Universe is:• cold

• non-baryonic

• neutral

• very weakly interacting

⇒Weakly Interacting Massive Particle

• stable due to the discrete symmetry

DM DM→ SM SM︸︷︷︸pair annihilation

, DM 6→ SM, ...︸︷︷︸stable

• annihilation cross-section 〈σv〉 ∝ EW interaction

• thermal evolution of DM density – a fixed value after freeze-out

3 / 24


Higgs-portal DM

Simplest realisation: the SM with ΦSM + Z2-odd scalar S:

S → −S, SM fields→ SM fields

L = LSM +1

2(∂S)2 − 1

2m2DMS

2 − λDMS4 − λSShΦ2SMS

2

SM sectorHiggs←→ DM sector

DM

DM

hSM

N N

DM DM

hSM

SM

SM

DM

DM

hSM

⟨σv⟩ σDM−N ΓinvhSM

given by the same coupling

Strong constraints from relic density + direct detection + Higgs decays

⇒ modified Higgs-portal-type DM candidates in multi-scalar models

in this talk: focus on DM phenomenology in the I(2+1)HDM i.e.

3HDM with Two Inert and One Higgs doublet

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I(2+1)HDM

Z2-symmetry in I(2+1)HDM:

φ1 → −φ1, φ2 → −φ2, φ3 → φ3, SM fields→ SM fields

Z2-invariant potential:

V =3∑i

[−|µ2

i |(φ†iφi) + λii(φ†iφi)

2]

+3∑ij

[λij(φ

†iφi)(φ

†jφj) + λ′ij(φ

†iφj)(φ

†jφi)

]+(−µ2

12(φ†1φ2) + λ1(φ†1φ2)2 + λ2(φ†2φ3)2 + λ3(φ†3φ1)2 + h.c.)

+(λ4(φ†3φ1)(φ†2φ3) + λ5(φ†1φ2)(φ†3φ3) + λ6(φ†1φ2)(φ†1φ1)

+ λ7(φ†1φ2)(φ†2φ2) + λ8(φ†3φ1)(φ†3φ2) + h.c.)

• 21 parameters in V

• µ212, λ1, λ2, λ3 are complex

• Yukawa interaction: ”Model I”-type (only φ3 couples to fermions)

• explicit Z2-symmetry

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Parameters of V

• µ23 = v2λ33 = m2

h/2 fixed from extremum conditions

• ”dark democracy”: µ21 = µ2

2, λ13 = λ23, λ′13 = λ′23, λ3 = λ2, e.g.

λ2(φ†2φ3)2 + λ3(φ†3φ1)2 + h.c.→ λ2

((φ†2φ3)2 + (φ†3φ1)2 + h.c.

)•(λ4(φ†3φ1)(φ†2φ3) + λ5(φ†1φ2)(φ†3φ3) + ...

): no new phenomenology

2M ⇒ λ4−8 = 0

• λ1, λ11,22,12, λ′12 – self-interactions of inert doublets

21 parameters → 7 important parameters

• µ22 – mass scale of inert particles

• µ212 = |µ2

12|eiθ12 , λ2 = |λ2|eiθ2 – mass splittings and CPv phase

• λ2, λ23, λ′23 – DM-Higgs coupling

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DM in I(2+1)HDM

Z2-invariant vacuum state:

φ1 =

(H+

1

H01+iA0

1√2

), φ2 =

(H+

2

H02+iA0

2√2

), φ3 =

(G+

v+h+iG0√

2

)

• φ3 – SM-like doublet with SM-like Higgs h

• Z2-odd doublets φ1 and φ2 mix:

S1 =αH0

1 + αH02 −A0

1 +A02√

2α2 + 2, S2 =

−H01 −H0

2 − αA01 + αA0

2√2α2 + 2

S3 =βH0

1 − βH02 +A0

1 +A02√

2β2 + 2, S4 =

−H01 +H0

2 + βA01 + βA0

2√2β2 + 2

H±1 =e±iθ12/2√

2(S±1 − S

±2 ), H±2 =

e∓iθ12/2√2

(S±1 + S±2 )

• 4 neutral and 4 charged Z2-odd particles (double the IDM)

• S1 – DM candidate, other dark particles heavier

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Physical Parameters

Parameters of V : µ22, |λ2|, |µ2

12|, λ23, λ′23, θ12, θ2

Physical parameters:

DM mass:

mS1

Mass splittings:

δ12 = mS2 −mS1

δ1c = mS±1−mS1

δc = mS±2−m

S±1

Higgs-DM coupling:

gS1S1h

CPv phases:

θ12, θ2

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Benchmark scenarios

This talk: mS1 < mZ :

A1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 1.5

mS1 < mS2,3,4 ,mS±1,2

(no coannihilation)

B1 : δ12 = 125 GeV, δ1c = 50 GeV, δc = 50 GeV, θ2 = θ12 = 0.82

mS1 ≈ mS3 < mS2,4 ,mS±1,2

C1 : δ12 = 12 GeV, δ1c = 100 GeV, δc = 1 GeV, θ2 = θ12 = 1.57

mS1 ≈ mS3 ≈ mS4 ≈ mS2 < mS±1,2

Checked against experimental and theoretical constraints:details in JHEP 1612 (2016) 014

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DM Annihilation for light DM

S1

S1

h

f

f

Higgs-mediated annihilation

depends on mS1 and gS1S1h

S1

Sj

Z

f

f ′

Z-mediated coannihilation

depends on mSj −mS1 :

A1: no coannihilation

B1: S1S3 coannihilation only

C1: S1S3, S2S4, S1S4, S2S3 coann.

depends on ZSiSj couplings

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Z-inert couplings

χZS1S3 = χZS2S4 = α+β√α2+1√β2+1

, χZS1S4 = χZS2S3 = αβ−1√α2+1√β2+1

,

χ2ZS1S3

+ χ2ZS1S4

= 1, χ2ZS2S3

+ χ2ZS2S4

= 1

50 60 70 80 90

mS1 [GeV]

-1.0

-0.8

-0.6

-0.4

-0.2

gSi Sj Z

CPC

A1:ZS1S3

A1:ZS1S4

B1:ZS1S3

B1:ZS1S4

C1:ZS1S3

C1:ZS1S4

• mass order: mS1 < mS3 < mS4 < mS2

• CPc value χZS1S3 = −1, χZS1S4 = 0

• ZS1S3 – reduced; 20− 50% for A1, B1, ∼ 0 for C1• ZS1S4 – close to the CPc value → dominant channel for C1

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Low DM mass

45 50 55 60ms1

[GeV]

-0.2

-0.1

0.1

0.2

gS1 S1 h

A1

B1

C1

A1: mainly Higgs annihilation, large gS1S1h

B1: Higgs annihilation (smaller gS1S1h)

B1: + ZS1S3 coannihilation (reduced with respect to the CPc case)

C1: mainly ZS1S4 coannihilation (χZS1S4 ≈ −1)

C1: + Higgs annihilation

Tools used in calculation: LanHEP, arXiv:1412.5016 [physics.comp-ph]; CalcHEP 3.4, Comput. Phys.

Commun. 184 (2013) 1729;micrOMEGAs 4.2 arXiv:1407.6129 [hep-ph]

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Medium DM mass

Main annihilation channels into gauge bosons V = W±, Z:S1

S1

h

V

V

gS1S1h, ge

S1

S1

V

V

gV V S1S1 =g2e

2 sin2 θW

no dependence on the benchmarks

65 70 75 80 85 90ms1

[GeV]

-0.3

-0.2

-0.1

0.1

0.2

0.3

gS1 S1 h

A1

B1

C1

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Filling the plot

50 60 70 80 90ms1

[GeV]

-0.2

-0.1

0.1

0.2

gS1 S1 h

CPC

B2

B3

B4

Other

mS1 < mh/2: many new solutions:

mS1 < mh/2: different mass splittings + ZSiSj interaction strength

mS1 > mh/2: less freedom but still new solutions:

mS1 > mh/2: Higgs mediated coannihilation + sign of hS3S3 coupling

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Direct detection

σS1,N ∝g2S1S1h

(mS1+mN )2

10-39

10-38

10-37

40 50 60 70 80 90

mS1 [GeV]

10-1510-1410-1310-1210-1110-1010-910-810-710-6

σS1,N

[pb

]

A1B1C1

LUX (2016)XENON1T

ν scattering

Case A1: mostly excluded (large gS1S1h)

Cases B1 and C1: mostly within the limits

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Indirect detection

10-33

10-32

10-31

10-30

10-29

10-28

10-27

10-26

10-25

40 50 60 70 80 90

〈vσ〉

[cm

3/s

]

mS1 [GeV]

A1B1C1

Fermi-LAT (bb-)

Most of the parameters space in agreement with Fermi-LAT

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LHC constraints

Higgs invisible decays

Γ(h→ S1S1) =g2S1S1hv

2

32πmh

(1−

4m2S1

m2h

)1/2

, Br(h→ inv) = Γ(h→S1S1)

ΓSMh

+Γ(h→S1S1)

Higgs total decay

µtot = BR(h→XX)BR(hSM→XX)

=ΓSMtot (h)

ΓSMtot (h)+Γinert(h)

LHC limits

µtot = 1.17± 0.17 and Br(h→ inv) < 0.2

45 50 55 60ms1

[GeV]-0.2

-0.1

0.0

0.1

0.2

gS1 S1 h

case A1

μmintot(h)=0.66

Br(h→inv)=0.20

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LHC constraints

45 50 55 60ms1

[GeV]-0.2

-0.1

0.0

0.1

0.2

gS1 S1 h

case B1

μmintot(h)=0.66

Br(h→inv)=0.20

45 50 55 60ms1

[GeV]-0.2

-0.1

0.0

0.1

0.2

gS1 S1 h

case C1

μmintot(h)=0.66

Br(h→inv)=0.20

In general: scenarios of type C are the least constrained.

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Conclusions and Outlook

• 3HDM with Z2 symmetry: I(2+1)HDM

• viable DM candidate

• large dark sector: important coannhilation effects in ΩDMh2

ala → varying strength of gauge-inert couplings

ala → new regions in agreement with Planck

• agreement with direct and indirect detection limits:

45 GeV . mS1 . 62.5 GeV, 64 GeV . mS1 . 74 GeV, mS1 & 400 GeV

→ as long as DM is practically invisible

→ other detections prospects?

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Inert cascade decays at the LHC

work in progress

pp→ Z → S2,3,4S1 → S1S1Z∗ → S1S1e

+e−

S2,3,4

Z∗e−

e+

S1

• signature: missing ET and dilepton pair

• dominant if there is a large mass splitting between DM and otherinert particles

• process present in the IDM (through HAZ vertex)

• note: possible differences with respect to the IDM due to varyingstrength of S1SjZ vertex

20 / 24


Inert cascade decays at the LHC

work in progress

pp→ h→ S2,3,4S1 → S1S1γ∗ → S1S1e

+e−

S2,3,4

S+

S1

W+

S+

γ∗

S2,3,4

S1

γ∗

S+

W+

• signature: missing ET and dilepton pair

• important if there is a small mass splitting between DM and otherinert particles → scenario C is preferred anyway

• process absent in the IDM (no A→ Hγ∗ loop)

• promising preliminary results σ ∼ 10−5 pb

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DM self-couplings

Dark self-couplings – no impact on standard DM and LHC phenomenology

• In the I(1+1)HDM – λ2

• In the I(2+1)HDM – λ1, λ11,22,12, λ′12

• Possible relevant corrections to loop processes, e.g.:

D

D γD+

γ

D

D D+

h

f

f

D – DM matter, D± – charged dark scalar

• Astrophysical DM detection experiments:

DM very weakly coupled to the visible sector

⇒ loop corrections can be important!

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Final Summary

Scalar DM models:

• interesting phenomenology

• strong constraints on gDMh from DM experiments

• need to move away from Higgs-portal

• solution: rich particle spectrum & coannihilation effects

• interesting LHC signatures – a tool for testing DM models?

• loop processes & role of self-couplings – can be important

• Further work needed!

23 / 24


References

• Higgs-portal DM models[B. Patt and F. Wilczek, hep-ph/0605188, X. Chu, T. Hambye, and M. H. Tytgat, JCAP 1205

(2012) 034, A. Djouadi, O. Lebedev, Y. Mambrini, and J. Quevillon, Phys.Lett. B709 (2012)

65–69]

• 3HDM[V. Keus, S. King, S. Moretti JHEP 1401 (2014) 052, arXiv:1408.0796; V. Keus, S. F. King,

S. Moretti and D. Sokolowska, JHEP 1411 (2014) 016, JHEP 1511, 003 (2015)]

• Experimental constraints[ATLAS and CMS collaborations, JHEP 08 (2016) 045; http://lux.brown.edu/LUX_dark_matter/Talks_

files/LUX_NewDarkMatterSearchResult_332LiveDays_IDM2016_160721.pdf(“Dark-matter results from 332 new

live days of LUX data, Identification of Dark Matter, The University of Sheffield, Sheffield, UK,

21 July, 2016”), M. Ackermann et al. [Fermi-LAT Collaboration], Phys. Rev. Lett. 115 (2015)

23, 231301, XENON1T Collaboration, Springer Proc. Phys. 148 (2013) 93 ]

• Numerical Tools[LanHEP, arXiv:1412.5016 [physics.comp-ph]; CalcHEP 3.4, Comput. Phys. Commun. 184

(2013) 1729; micrOMEGAs 4.2 arXiv:1407.6129 [hep-ph]]

24 / 24

http://lux.brown.edu/LUX_dark_matter/Talks_files/LUX_NewDarkMatterSearchResult_332LiveDays_IDM2016_160721.pdf

http://lux.brown.edu/LUX_dark_matter/Talks_files/LUX_NewDarkMatterSearchResult_332LiveDays_IDM2016_160721.pdf

BACKUP SLIDES

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Heavy DM

400 500 600 700 800ms1

[GeV]

-0.6

-0.4

-0.2

0.2

0.4

0.6

gS1 S1 h

H1

G1

• gS1S1h in Case G > gS1S1h Case H

• The same behaviour in both cases

• Lower mS1 for Case G

• Not really different from the CPc case

26 / 24

Direct Detection

σDM,N ∝g2S1S1h

(MS1+MN )2

400 500 600 700 800mS1 [GeV]

10-15

10-13

10-11

10-9

σ(DM,N [pb]

LUX

XENON 1T

ν scattering

case G1

case H1

• in agreement with LUX

• within the reach of XENON-1T

• case G (bigger couplings) easier to see/exclude than case H (smallercouplings)

27 / 24

Mass formulas

m2

S±1

= (−µ22 − |µ2

12|) +1

2λ23v

2, m2

S±2

= (−µ22 + |µ2

12|) +1

2λ23v

2.

m2S1

=v2

2(λ′23 + λ23)− Λ− µ2

2,

m2S2

=v2

2(λ′23 + λ23) + Λ− µ2

2,

m2S3

=v2

2(λ′23 + λ23)− Λ′ − µ2

2,

m2S4

=v2

2(λ′23 + λ23) + Λ′ − µ2

2,

Λ =√v4|λ2|2 + |µ2

12|2 − 2v2|λ2||µ212| cos(θ12 + θ2),

Λ′ =√v4|λ2|2 + |µ2

12|2 + 2v2|λ2||µ212| cos(θ12 + θ2).

α =−|µ2

12| cos θ12 + v2|λ2| cos θ2 − Λ

|µ212| sin θ12 + v2|λ2| sin θ2

, β =|µ2

12| cos θ12 + v2|λ2| cos θ2 − Λ′

|µ212| sin θ12 − v2|λ2| sin θ2

.

28 / 24

Physical Basis

|µ212| =

1

2(m2

S±2−m2

S±1

),

λ23 =2µ2

2

v2+m2

S±2

+m2

S±1

v2,

λ′23 =1

v2(m2

S2+m2

S1−m2

S±2−m2

S±1

),

µ22 =

v2

2gS1S1h −

v2|λ2|2(1 + α2)

(4α sin θ2 + 2(α2 − 1) cos θ2

)−m2S2

+m2S1

2,

|λ2| =1

v2

[|µ2

12| cos(θ2 + θ12)+√|µ2

12|2 cos2(θ2 + θ12) +

(m2S2−m2

S1

2

)2

− |µ212|2

.

29 / 24

DM annihilation diagrams

Light DM annihilation:

S

S

h

f

f(a)

S

S′

V

f

f ′

(b)Virtual gauge bosons:

S

S′

h

V, V ∗

V, V ∗

(a)

S

S

V, V ∗

V, V ∗

(b)

30 / 24

DM annihilation diagrams - gauge limit

Heavy DM (co)annihilation diagrams with pure gauge boson final states:

S

S′

V

V ′

V ′′

(a)

S

S′

V

V ′

(b)

S

S′′

S′

V

V ′

+ crossed

(c)

31 / 24

DM annihilation diagrams

Heavy DM (co)annhilation channels involving the SM-like Higgs boson:

S

S′

h

V

V ′

(a)

S

S′

h

V

V ′

(b)

S

S′′

S′

V

h

+ crossed

(c)

S

S′

h

h

h(d)

S

S′

h

h(e)

S

S′′

S′

h

h

+ crossed

(f)

32 / 24

Relic density

-0.2 -0.1 0.0 0.1 0.2gS1 S1 h0.05

0.10

0.15

0.20

0.25

0.30ΩDMh

2

B1:mS1 = 45 GeV

A1:mS1 = 47 GeV

B1:mS1 = 47 GeV

B1:mS1 = 50 GeV

A1:mS1 = 53 GeV

-0.2 -0.1 0.0 0.1 0.2gS1 S1 h0.05

0.10

0.15

0.20

0.25

0.30ΩDMh

2

A1:mS1 = 69 GeV

A1:mS1 = 75 GeV

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Higgs-inert couplings

50 60 70 80 90

mS1 [GeV]

0.02

0.04

0.06

0.08

0.10

0.12

gSi Sj h

gS1 S1 h=0.001

hS1S1

B1:hS3S3

C1:hS1S2

C1:hS2S2

C1:hS3S3

C1:hS3S4

C1:hS4S4

34 / 24

Documents

Scalar Dark Matter candidate in Multi-Higgs Modelsmoriond.in2p3.fr/QCD/2017/SundayMorning/Sokolowska.pdf · MotivationI(2+1)HDM mS 1 < mZ LHCConclusion Scalar Dark Matter candidate