Dark Matter in scalar extensions of the Standard Model

Dark Matter in scalar extensions of the Standard Model

Dorota Sokołowska

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

ICHEP 2014 Valencia, Spain, 03.07.2014

based on work in progress with Venus Keus, Steve F. King, Stefano Moretti (University of Southampton)

Higgs particle discovered

• a Higgs boson has been discovered at the LHC

• VERYSM-like:

→Higgs signal strength≈1 (within experimental accuracy) ATLAS:Mh= 125.5GeV, µ^tot= 1.30^+0.18_−0.17

CMS:Mh= 125.7GeV, µ^tot= 0.80^+0.14_−0.14

→strong constraints for extensions of the Standard Model...

• yet we do expect some New Physics to exist

• neutrino masses

• baryon asymmetry and baryogenesis

• vacuum stability

• Dark Matter

• ...

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Dark Matter

Evidence 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

⇒WeaklyInteractingMassiveParticle

• stable due to the discrete symmetry

• standard particle physics’ candidate: neutralino ala→but no sign of SUSY at the LHC ala→a scalar candidate?

Higgs-portal DM

Simplest realization: SM+Z2-odd scalarS:

S→ −S, SM fields→SM fields

L=LSM+ (∂S)²−gDM hh^SMS² Higgs-portal interaction:

SM sector^Higgs←→ DM sector

DM

DM h^SM

N N

DM DM

h^SM SM

SM DM

DM h^SM

⟨σv⟩ σ_DM−N Γ^inv_hSM

given by the same coupling

Strong constraints from relic density+direct detection+Higgs decays

[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]

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Multi-Higgs Doublet Models

• two or more scalarSU(2)W doublets

• rich phenomenology: various Yukawa couplings, CP violation in the scalar sector, different types of vacua, phase transitions in the early Universe, baryogenesis,...

• 2HDM with an exactZ2 symmetry: Inert Doublet Model (IDM) 2H→SM-like Higgs boson

2H2HDM→modifications of the diphoton decay rate possible 2H→a Dark Matter candidate

2H→well studied and understood

[N. G. Deshpande, E. Ma, PRD 18 (1978) 2574, J. F. Gunion, H. E. Haber, G. Kane, S. Dawson, The Higgs Hunter’s Guide, 1990 Addison-Wesley, R. Barbieri, L. J. Hall, V. S. Rychkov, PRD 74 (2006) 015007, I. F. Ginzburg, K. A. Kanishev, M. Krawczyk, D. Sokolowska, PRD 82 (2010) 123533]

• 3HDM with an exactZ2 symmetry

2H→many features of the IDM with new phenomena

• within the reach of current and future experiments

Scalar DM at the LHC

•direct & indirect detection: not a coherent picture of Dark Matter

• tension between DAMA, CoGeNT, CRESST-II, CDMS-II, XENON100, LUX & lack of proven indirect detection signals

•LHC results

• mass of the Higgs boson: Mh≈125GeV

• Higgs phenomenology – sensitive to ”new physics”

• a Higgs portal DM – interaction throughh

•We want to use

(a)the relic densityΩDMh² (3σPlanck)

0.1118<ΩDMh²<0.128

[Planck Collaboration, P. Ade et. al., Planck 2013 results. XVI. Cosmological parameters]

(b)Higgs invisible decays(ATLAS/CMS & global fits) Br(h→inv).20−35%

[G. Belanger, B. Dumont, U. Ellwanger, J. F. Gunion, S. Kraml, PLB 723 (2013) 340;

ATLAS-CONF-2014-010, 2014; CMS-PAS-HIG-14-002]

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3HDM

work in progress with V. Keus, S.F. King, S. Moretti Z2-symmetryin 3HDM:

φ1→ −φ1, φ2→ −φ2, φ3→φ3, SM fields→SM fields Z2-invariant potential:

V =

3

X

i

h−|µ²i|(φ^†_iφi) +λii(φ^†_iφi)²i +

3

X

ij

h

λij(φ^†_iφi)(φ^†_jφj) +λ⁰ij(φ^†_iφj)(φ^†_jφi)i +

−µ²12(φ^†₁φ2) +λ1(φ^†₁φ2)²+λ2(φ^†₂φ3)²+λ3(φ^†₃φ1)²+h.c

• all parameters real

• Yukawa interaction: ”Model I”-type (onlyφ3 couples to fermions)

• explicitZ2-symmetry

• µ²₁₂6= 0⇒mixing betweenφ1 andφ2

Multi-Inert 3HDM

Z2-invariant vacuum state:

φ1=

H⁺₁ H₁⁰+iA⁰₁

√ 2

!

, φ2=

H₂⁺ H₂⁰+iA⁰₂

√ 2

!

, φ3=

H₃⁺ v+H₃⁰+iA⁰₃

√ 2

!

• φ3 – SM-like doublet with SM-like HiggsH3⁰

• Z2-odd doubletsφ1 andφ2 mix:

H1= cosαHH₁⁰+ sinαHH₂⁰, H2= cosαHH₂⁰−sinαHH₁⁰

(similar forAi andH_i^±)

• 4 neutral and 4 chargedZ2-odd particles (double the IDM)

• H1–DM candidate, other dark particles heavier

• Note: V 3

−µ²₁₂(φ^†₁φ2) +λ1(φ^†₁φ2)²+λ2(φ^†₂φ3)²+λ3(φ^†₃φ1)²+h.c 2M→term added to avoidZ2×Z2-symmetricV

2M→lifts degeneracy betweenHiandAi!

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Constraints

(1) Vacuum stability:

scalar potentialV bounded from below (2) Perturbative unitarity:

eigenvaluesΛiof the high-energy scattering matrix fulfil|Λ_i|<8π (3) Higgs mass:

Mh= 125GeV (4) EWPT & LEP:

M_H±

i &70−90GeV, MH_i+MA_i> MZ

(5) HHH111 as DM candidate:

MH< MA, M_H± and0.1118<ΩDMh²<0.128(3σPlanck)

(6) Indirect DM detection: Fermi & HESS (7) Direct DM detection: LUX

(8) Higgs invisible decays: ATLAS & CMS & global fits Br(h→inv).20−35%

Dark Matter in 3HDM

• annihilation through Higgs into fermions

f

f¯ H1

H1 h^SM

depends ongDM h coupling; dominant channel forMDM< Mh/2

• annihilation into gauge bosons (also into virtual states)

H1

H1

V

V h^SM

H1

H1

V

V and

H1

H1

V^∗ V^∗ H1

H1

V V^∗

crucial for heavy masses; non-negligible forMh/2< MDM< MW

• coannihilation

f f¯ H1

H2

h^SM

f f^′ H1

A1, A2

Z^∗

f f^′ H1

H1^±, H2^±

W^±∗

very important when particles have similar masses

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LHC and direct detection

DM-scattering on nucleus through the Higgs exchange

σDM−N∝g_{DM h}² /(MH₁+MN)²

Higgs invisible decays forMDM < Mh/2

Γ(h→H1H1) =^g_32πM^{2DM hv2}

h

r 1−^4M

2 H1 M_h²

3HDM as (almost) Higgs portal model

ForMDM< Mh/2:

DM

DM h^SM

N N

DM DM

h^SM SM

SM DM

DM h^SM

⟨σv⟩ σDM−N Γ^inv_hSM

Tension:

• proper relic density↔largehσvi ↔largegDM h

• direct detection↔smallσDM−N ↔smallgDM h

• LHC↔smallBr(h→inv)↔smallgDM h

Solution:

destroy the Higgs-portal type relation between hσvi, σDM−N,Γ(h→inv)

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DM annihilation in 3HDM

•Possible scenarios forMH₁< MW:

(A) no coannihilation effects: MH₁< M_H

2,A₁,A₂,H^±₁,H₂^±

(B) coannihilationwithH2: MH₁≈MH₂ < M_A

1,A₂,H^±₁,H^±₂

usually relic density too big

(C) coannihilationwithA1: MH₁≈MA₁< M_H

2,A₂,H^±₁,H₂^±

usually relic density too small (D) coannihilationwithH2, A1, A2:

coannihilationnnmmmm,MH₁≈MA₁ ≈MH₂≈MA₂ < M_H± 1,H₂^±

•IfMH₁ heavier (to escape LEP limit forH^±) also coannihilation withH_i^±.

•Toy Modelwith additional ”symmetry”:

µ²₁=µ²₂, λ13=λ23, λ⁰₁₃=λ⁰₂₃, λ3=λ2

H1= 1

√2(H1⁰+H2⁰), H2= 1

√2(H2⁰−H1⁰)

Relic density: M

/2 GeV < M

< M

/2 GeV

MA1 =MH1+δ ; MH2 =MH1+∆

-0.2 -0.1 0.0 0.1 0.2gDMh 0.1

0.2 0.3 0.4 0.5 W_DMh²

HALd>50,D=50 ⁴⁵

48 50 51 52 53 55 58

62 -0.10 -0.05 0.00 0.05 0.10 g_DMh 0.05

0.10 0.15 0.20

W_DMh²

HDLd=7,D=1 ⁴⁵

47 48 49 51 52 53 55 59

no coannhilation coannhilation withH2, A1,2

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Planck constraints: M

< M

/2

Relic density constraints (PLANCK)

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

40 45 50 55 60

gDMh

DM mass Case A Excluded

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

46 48 50 52 54 56 58 60

gDMh

DM mass Case D Excluded

Case A(no coannhilation) – coupling bigger than inCase D(with coannihilation)

Planck constraints: M

> M

/2

Relic density constraints (PLANCK)

-0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

62 64 66 68 70 72 74 76 78

gDMh

DM mass Case A Excluded

-0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

62 64 66 68 70 72 74 76 78

gDMh

DM mass Case D Excluded

Case AandCase Dslightly different

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Direct detection

10^-54 10^-52 10^-50 10^-48 10^-46 10^-44 10^-42

45 50 55 60 65 70 75 80

σDM,N [cm2]

M_DM

Preliminary LUX Case A Case D

Case D: new region in agreement with LUX with respect toCase A sign of coannhilation effects

LHC constraints

Br(h→inv)≈

P

i,jΓ(h→XiXj) Γ^SM(h) +P

i,jΓ(h→XiXj)

0 10 20 30 40 50 60

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06

MH1

gDMh

BrHh®invL=0.37 BrHh®invL=0.20

0 10 20 30 40 50 60

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06

MH1

gDMh

BrHh®invL=0.37 BrHh®invL=0.20

case A case D

• Br(h→inv)<37%⇒

ala• |gDM h|.0.02for Case A • −0.015.gDM h.0for Case D

• Br(h→inv)<20%⇒

ala• |gDM h|.0.015for Case A •strong constraints for Case D!

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LHC vs Planck

50 55 60 MH1

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

gDMh

BrHh®invL=0.37 BrHh®invL=0.20

50 55 60 MH1

-0.04 -0.02 0.00 0.02 0.04

gDMh

BrHh®invL=0.37 BrHh®invL=0.20

case A case D

• Br(h→inv)<37% & ΩDMh²⇒

ala•MDM&53GeV for Case A • almost all masses ok for Case D

• Br(h→inv)<20% & ΩDMh²⇒

ala•MDM&53GeV for Case A •MDM &53GeV for Case D

Conclusions

• 3HDMwithZ2 symmetry: good DM candidate

• large dark sector

ala→important coannhilation effects inΩDMh²

• Case D with multiple coannihilation channels ala→new viable region in agreement with LUX

• LHC constraints – strong forMH1< Mh/2

ala→stronger than direct detection limits!

• further study – heavy DM

• additional symmetries? multi-component DM?

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BACKUP SLIDES

MA₂=MH₂+δ;MX₁=MX₂+∆

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Direct detection + LHC

10^-54 10^-52 10^-50 10^-48 10^-46 10^-44 10^-42

45 50 55 60 65 70 75 80

σDM,N [cm2]

M_DM

Preliminary BR(inv)=0.2LUX BR(inv)=0.37 Case A Case D

For the SM:

V =λφ⁴

βλ∼(λ²−y⁴t+...)⇒ λnegative at large scales

[Butazzo et al (arXiv:1307.3536)]

10² 10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ 10¹⁸ 10²⁰ -0.04

-0.02 0.00 0.02 0.04 0.06 0.08 0.10

RGE scaleΜin GeV

HiggsquarticcouplingΛ

3Σbands in Mt=173.1± 0.6 GeVHgrayL Α₃HM_ZL=0.1184±0.0007HredL

M_h=125.7± 0.3 GeVHblueL

M_t=171.3 GeV

Α_sHM_ZL=0.1163 ΑsHM_ZL=0.1205

Mt=174.9 GeV

Additional scalar states⇒ additionalpositivecontributions toβλ

[for example: SM + singlet, arXiv:0910.3167]

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