An update on the two singlet Dark Matter model

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An update on the two singlet Dark Matter model

Dr.Tanushree Basak (Indus University)

Co-authors : Dr. Baradhwaj Coleppa (IIT, Gandhinagar), Mr. Kousik Loho (IIT, Gandhinagar) Ref. JHEP06(2021)104

TAUP 2021 - Parallel Session

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The Two-singlet Model

Model : SM + Two singlets (S1 & S2) ImposedZ₂×Z₂⁰ symmetry

SM : even under both Z₂ & Z₂⁰ symmetry and the rest transform as, S₁−→ −S^Z² ₁,S₁ ^Z

0

−→2 S₁, S2

Z2

−→S2,S2 Z₂⁰

−→ −S₂

Z₂ symmetry : broken spontaneously

Z₂⁰ symmetry : unbroken and ensures the stability ofS₂ (Dark matter candidate)

Scalar Lagrangian of the model : L_s = (D^µΦ)^†D_µΦ +1

2∂^µS₁∂_µS₁+1

2∂^µS₂∂_µS₂−V(Φ,S₁,S₂)

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The Two-singlet Model

Scalar Potential : V =−m²₀

2 (Φ^†Φ)−m²₁

2 S₁²+m₂²

2 S₂²+λ₀

4 (Φ^†Φ)²+λ₁ 4 S₁⁴ +λ2

4 S₂⁴+λ₀₁(Φ^†Φ)S₁²+λ₀₂(Φ^†Φ)S₂²+λ₁₂S₁²S₂² After symmetry breaking,

Φ = 1

√2 0

v₀+h₀

; S₁=v₁+h₁

Mass matrix for the scalar sector : M_s = h0 h1

^λ⁰^v

2 0

4 λ01v0v1

λ₀₁v₀v₁ λ₁v₁²

! h₀ h1

+1

2(m₂²+λ02v₀²+ 2λ12v₁²)S₂²

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The Two-singlet Model

Mass eigenstatesh andH and the mixing angle α tan 2α= 2λ₀₁v₀v₁

λ0v₀²

4 −λ₁v₁² Quartic self-couplings λ0 andλ1 :

λ₀ = 2 v₀²

m²_h+m_H²

2 +

s

(m_h²−m²_H)²

4 −4λ²₀₁v₀²v₁²

,

λ1 = 1 2v₁²

m²_h+m²_H

2 −

s

(m²_h−m²_H)²

4 −4λ²₀₁v₀²v₁²

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Constraints

All theoretical and experimental constraints to be imposed upon the parameter space

Analyze and scan the parameter space of the couplings (λ₀₁,λ₀₂, λ12) and put bounds on their values from various constraints Two choices: (i) fixing the lighter scalar : SM Higgs and m_H = 250 GeV and (ii) choosing the heavier scalar : SM Higgs andm_h= 80 GeV.

Major constraints : Vacuum stability Collider constraints LHC Higgs searches

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Vacuum Stability : Bound on coupling λ

01

v1=1 TeV v1=0.5 TeV v1=0.3 TeV

0.00 0.01 0.02 0.03 0.04

0.40 0.45 0.50

λ01 λ0

mh=80 GeV,mH=125 GeV

0.00 0.01 0.02 0.03 0.04

0.00 0.01 0.02 0.03 0.04 0.05 0.06

λ01 λ1

0.00 0.05 0.10 0.15 0.20

1.4 1.6 1.8 2.0

λ01 λ0

0.00 0.05 0.10 0.15 0.20

λ01 λ1

Bound onλ₀₁: (Top/Bottom left) Due to positivity constraints onλ₀forv₁: 1 TeV, 0.5 TeV and 0.3 TeV and that onλ₁ (Top/Bottom right) for them_H= 125(m_h= 125) GeV case for the same set ofv₁values.

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Collider Constraints

Branching Ratio (BR) of the Higgs invisible decays:

BR_h→inv = Γh→inv

Γh→SM+ Γh→inv

Case 1 : m_H = 125 GeV with both h andS₂ lighter, both decays H →hh andH →S2S2 to be considered

Case 2 : mh= 125 GeV, only the decayh →S2S2 is relevant Fixing λ₀₁= 0.008 (0.04) form_H = 80 GeV (250 GeV) : consistent with Vacuum stability

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Bound on coupling λ

12

v1=1.0 TeV v1=0.5 TeV v1=0.3 TeV

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.000

0.005 0.010 0.015 0.020 0.025

λ02 λ12

v1=1.0 TeV v1=0.5 TeV v1=0.3 TeV

0.00 0.05 0.10 0.15 0.20 0.25

0.000 0.005 0.010 0.015 0.020

λ02 λ12

m_h=125 GeV,m_H=250 GeV

Contours of BR=11% forv1= 1 TeV, 0.5 TeV and 0.3 TeV form_H= 125 GeV (left) andm_h= 125 GeV case (right). The allowed region for them_h= 125 GeV case on the right is the band between the corresponding lines.

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LHC Higgs searches

σ(gg->H->WW)for 13 TeV

σ(gg->H->ZZ)for 8 TeV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0 0.2 0.4 0.6 0.8

λ₀₂ λ12

σ(gg->H->WW)for 13 TeV

0.00 0.05 0.10 0.15 0.20 0.25

0.00 0.05 0.10 0.15 0.20

λ02 λ12

Allowed regions in theλ₀₂−λ₁₂parameter space : from searches for the heavy scalarHat the LHC in the diboson channel gg→H→WW/ZZwith the gauge bosons decaying either leptonically or hadronically (left) and a magnified view of the 13

TeV constraints (right).

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Dark matter phenomenology : Direct detection

Effective lagrangian for nucleon-dark matter interaction : L_eff =a_NNNS¯ ₂²

Spin independent scattering cross-section : σ^SI_N = µ²

4πm_S²

2

λ_HS₂_S₂ m_H²

X

q=u,d,s

mq

v₀ cosαm_N

m_qf_Tq^N + 2

27f_TG^N X

q=c,b,t

mq

v₀ cosαm_N m_q

−λhS2S2

m²_h

X

q=u,d,s

mq

v0

sinαmN

mq

f_Tq^N + 2

27f_TG^N X

q=c,b,t

mq

v0

sinαmN

mq

2

where the reduced mass µ= _m^m^N^m^S²

N+mS2.

Assumption of the quark contribution being approximately equal for both the nucleons (i.e.,f_Tq⁽ⁿ⁾≈f_Tq^(p)=f_Tq^N)

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Dark matter phenomenology : Benchmark Points

Benchmark Points :

Masses (GeV) λ₀₁ λ₀₂ λ₁₂ σ^SI_N(cm²) BP-1 mh= 80,mH= 125 0.008 0.002 0.0010 3.86×10⁻⁴⁷ BP-2 m_h= 80,m_H= 125 0.008 0.002 0.0005 2.61×10⁻⁴⁹ BP-3 mh= 125,mH = 250 0.04 0.010 0.001 1.98×10⁻⁴⁷ BP-4 m_h= 125,m_H = 250 0.04 0.005 0.0006 2.35×10⁻⁴⁸

Representative benchmark points shown along with the corresponding spin independent cross-section values for a dark matter mass of 40 GeV andv₁= 1000 GeV.

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Dark matter phenomenology : Direct detection

BP-1 BP-2 LUX

Xenon1T-2σ Xenon1T

20 40 60 80 100

10-49 10-48 10-47 10-46

mS2(GeV) σNSI(cm2)

BP-3 BP-4 LUX Xenon1T-2σ Xenon1T

20 40 60 80 100

5.×10^-49 1.×10^-48 5.×10^-48 1.×10^-47 5.×10^-47 1.×10^-46 5.×10^-46

m_S 2(GeV) σNSI(cm2)

Variation ofσ_N^SI(cm²) withm_S₂(GeV) for the benchmark points - overlaid on the plots are the constraints from the Xenon-1T and LUX results.

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Dark matter phenomenology : Relic abundance

Relic Abundance :

Ωh² = 1.07×10⁹ x_f

√g^∗mplhσvi

where xf = ^m_T^S²,mpl is the Planck mass.

DM annihilates to SM particles only through scalar portal interactions Relevant channels : s-channel diagrams withh and H as propagators andbb,¯ ττ¯,W⁺W⁻,ZZ,hH,hh andHH as final states

For DM mass around 40 Gev, dominant contributions to the annihilation cross section will arise from thebb¯ andττ¯channels Breit-Wigner resonance : plays an important role in enhancing the velocity averaged cross section of DM-DM annihilation

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Dark matter phenomenology : Plot of w (s ) vs. m

S₂

b BP-1 τ_BP-1

40 50 60 70 80

0 5.×10^-8 1.×10^-7 1.5×10^-7

m_S2(GeV) w(s)b,τ

b BP-3 τBP-3

60 80 100 120 140 160

0 1.×10-8 2.×10-8 3.×10-8 4.×10-8 5.×10-8 6.×10-8

mS2(GeV) w(s)b,τ

Plot ofw(s) vs.m_S₂showing the contribution ofbbandτ τchannels. The two resonances correspond tom_h= 80 GeV and m_H= 125 GeV(left) andm_h= 125 GeV andm_H= 250 GeV(right)

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Dark matter phenomenology : Plot of Relic Abundance

BP-1 BP-2 Ωh²=0.120

40 50 60 70 80

10^-4 0.1 100

m_S2(GeV)

Ωh2

BP-3 BP-4 Ωh²=0.120

60 80 100 120 140 160

10^-7 0.001 10

m_S2(GeV)

Ωh2

Plot of relic abundance as a function of the DM mass. The horizontal dotted line shows the measured value of Ωh²= 0.120±0.001.

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Dark matter phenomenology : Gamma ray excess

BP-¹

<σv>_b^__b=³⨯10^-26cm³/^sec

<σv>_b^__b=¹⨯10^-26cm³/^sec

36 38 40 42 44 46 48 50

10^-²⁸ 10^-27 10^-26 10^-²⁵ 10^-²⁴ 10^-23

mS2(^GeV)

<σv>b_ b(cm3/sec)

Enhancement in thehσvi_b_¯_bvalues around resonance, shown here as a function of the dark matter mass.

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Conclusion

we studied a simple scalar extension of the SM with two real singlets S₁ andS₂ with aZ₂×Z₂⁰ symmetry

Z₂⁰ remains unbroken enabling the scalarS2 to be a viable dark matter candidate

Coupling λ01 is constrained to lie in the 10⁻¹−10⁻² range, by virtue of vacuum stability

Direct bounds from the Higgs invisible branching ratios forces λ₀₂≈10⁻²−10⁻³

Direct detection constraint is relaxed to a great extent by the destructive interference between the two t-channel h andH

propagators while the Breit-Wigner resonance helps to get the correct relic abundance

Two singlet model can also account for the gamma-ray excess for an S2 in the mass range 36−51 GeV

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