Gamma-ray Signatures of Scalar Dark Matter Takashi Toma Durham - - PowerPoint PPT Presentation

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Gamma-ray Signatures of Scalar Dark Matter Takashi Toma Durham - - PowerPoint PPT Presentation

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Gamma-ray Signatures of Scalar Dark Matter Takashi Toma Durham University Institute for Particle Physics Phenomenology (IPPP) Basis of the Universe with Revolutionary Ideas 2014 Toyama, Japan, 13-14 Feb. Based on T. T., arXiv:1307.6181,

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Gamma-ray Signatures of Scalar Dark Matter Takashi Toma

Durham University Institute for Particle Physics Phenomenology (IPPP)

Basis of the Universe with Revolutionary Ideas 2014 Toyama, Japan, 13-14 Feb.

Based on T. T., arXiv:1307.6181, Phys.Rev.Lett. 111 (2013) 091301,

  • A. Ibarra, T. T., M. Totzauer, S. Wild, in preparation

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 1 / 19

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Outline

Outline

Introduction Simple Model of Scalar Dark Matter Gamma-ray Signatures Summary

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 2 / 19

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Introduction

Indirect detection

In particular, γ-ray can be a characteristic signal of DM. · γ-ray flux

100 101 102 E [GeV] 10-7 10-6 10-5 E2 · dJ/dE [GeV/cm2 /s/sr]

  • C. Weniger, arXiv:1210.3013

· γ-ray excess around 130 GeV? · σvγ ∼ 10−27 cm3/s thermal DM ↔ 10−26 cm3/s · But Fermi Co. is negative. Significance is 1.6σ at 133 GeV.

Fermi Collaboration, arXiv: 1305.5597

This peak would be a fake, but it is still interesting to study a model which generates such a strong γ-ray. · We need better instruments.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 3 / 19

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Introduction Gamma-ray spectrum

Gamma-ray spectrum from dark matter annihilation

VIB box ΓΓ q q , Z Z , W W EE 0.15 EE 0.02 0.02 0.05 0.10 0.20 0.50 1.00 2.00 0.01 0.1 1 10

x E mΧ x2dNdx

Bringmann & Weniger 2012

  • T. Bringbann, C. Weniger arXiv:1208.5481

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 4 / 19

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Introduction Gamma-ray spectrum

Gamma-ray spectrum Line spectrum

  • ex. χχ → γγ, χχ → Zγ

suppression factor ∼ α2

em

Internal bremsstrahlung χχ → f f γ When chiral suppression is effective, it becomes important. suppression factor ∼ αem Box type spectrum

  • ex. χχ → SS → 4γ

(S: light mediator) if mχ ≫ mS, box type if mχ ≈ mS, Eγ ∼ mχ/2

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 5 / 19

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Introduction Thermal Dark Matter

Thermal relic of dark matter

Boltzmann equation: dn dt = −σv

  • n2 − n2

eq

  • σv = a + bv 2 + · · · ,

→ σv = a + b (6T/mχ) + · · · σvth ∼ 3 × 10−26 cm3/s ↔ Relic density Ωh2 = 0.12 For fermion DM, typically Internal bremsstraglung: σvf f γ ∼ 10−28 cm3/s Monochromatic gamma: σvγγ ∼ 10−30 cm3/s

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 6 / 19

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Model of Scalar Dark Matter

Model

Real singlet scalar χ (DM), Z2 = −1 Vector like charged fermion ψ (mediator), Z2 = −1, Y = −1 Interaction: LY = yχψPRf + h.c. V = m2

φφ†φ + m2 χ

2 χ2 + λφ 2

  • φ†φ

2 + λχ 4! χ4 + λ 2χ2 φ†φ

  • After φ gets VEV:

φ(x) = φ + h(x) √ 2 The coupling λ should be suppressed from the constraint of direct detection. σp = cλ2µ2

χm2 p

4πm2

χm4 h

7.6 × 10−46 [cm2]

LUX Collaboration, arXiv: 1310.8214

When mp ≪ mχ, the coupling is limited as λ 3.1 × 10−4.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 7 / 19

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Model of Scalar Dark Matter

Thermal relic density of DM

χχ → hh, χχ → h → f f are subdominant. The most important channel is χχ → f f mediated by ψ. The cross section is σvf f = y 4 4πm2

χ

m2

f

m2

χ

1 (1 + µ)2 − y 4 6πm2

χ

m2

f

m2

χ

1 + 2µ (1 + µ)4v 2 + y 4 60πm2

χ

1 (1 + µ)4v 4 + O(v 6), µ ≡ m2

ψ

m2

χ

· when mf ≪ mχ, s-wave and p-wave can be negligible. → chiral suppression · DM relic abundance is determined by d-wave.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 8 / 19

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Model of Scalar Dark Matter

Interpretation of d-wave

CP and total angular momentum J should be conserved between initial and final states. s-wave initial state: CP=even, J = 0 → possible effective operator: OS ∼ χχf f In our case, mf is multiplied to the operator. p-wave initial state: CP=odd, J = 1 J = 1 operator cannnot be constructed. OP ∼

  • χ∂µ

↔ χ

f γµf

  • = 0

Note: p-wave exists for complex scalar DM.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 9 / 19

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Model of Scalar Dark Matter

d-wave initial state: CP=even, J = 2 corresponding effective operator OD ∼ ∂µχ∂νχT µν T µν: energy momentum tensor An example of concrete models χ is related with radiative lepton masses

  • S. Baek, H. Okada, T. T, arXiv: 1401.6921

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 10 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Gamma-ray Signatures

Possible processes χχ → f f γ Internal bremsstrahlung

  • T. T, arXiv:1307.6181
  • F. Giacchino, L. Lopez-Honorez, M.H.G. Tytgat,

arXiv:1307.6480

χχ → γγ, χχ → Zγ Line spectrum

  • A. Ibarra, T. T, M. Totzauer, S. Wild, in preparation

Both gamma-ray emissions are ex- pected to be stronger than Majorana case since y is large enough.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 11 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Internal bremsstrahlung

· differential cross section

dσvf f γ dx = αemy 4 4π2m2

χ

(1 − x)

  • 2x

(µ + 1)(µ + 1 − 2x) − x (µ + 1 − x)2 −(µ + 1)(µ + 1 − 2x) 2(µ + 1 − x)3 log

  • µ + 1

µ + 1 − 2x

  • ,

x ≡ Eγ mχ

· When µ 4, a sharp peak appears around Eγ ∼ mχ · σvf f γ ∼ 10−27 cm3/s

10-2 10-1 100

x =E/mχ

10-3 10-2 10-1 100 101

x2 dN/dx µ + µ− (γ) τ + τ− (γ) ¯ bb(γ,g)

  • T. Bringmann et al., arXiv:1203.1312

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 12 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Line spectrum

χχ → γγ comes from box diagrams

ψ f f f χ χ γ γ f ψ ψ ψ χ χ γ γ ψ ψ f f χ χ γ γ

χχ → Zγ Zγ is related with γγ σvZγ ≈ 2 tan2 θW

  • 1 − 1

4 m2

Z

m2

χ

3 σvγγ The cross sections are typically σvγγ ≈ σvZγ ≈ 10−28 or 10−29 cm3/s when mχ 1000 GeV.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 13 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Calculation of χχ → γγ

In the limit of v → 0, it analytically can be calculated. Initial state: p1 = p2 = (mχ, 0) ≡ p, Final state: k1, k2 Flow of calculation

  • G. Bertone et al. arXiv:0904.1442

1 In general, iM is decomposed as

Mµν = pµpνA + kµ

1 kν 1 B + kµ 2 kν 2 C + · · · + g µνAloop

where iM = iǫ∗

µ(k1)ǫ∗ ν(k2)Mµν.

  • nly Aloop remains.

2 Simplify Aloop by Passarino-Veltman reduction 3 cross section:

σv = α2

emα2 y

2πm2

χ

|Aloop(µ)|2

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 14 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Aloop = 2 − 2 log µ − 1 µ

  • − 2µArcsin2

1 õ

  • ,

µ = m2

ψ/m2 χ > 1

  • S. Tulin et al. arXiv:1208.0009

The behavior is not good at µ ∼ 1. divergence

  • 2

2 4 6 8 1 1.5 2 2.5 3 3.5 4 Aloop µ

  • Ref. result

Our result Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 15 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Energy spectrum

0.1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 dNγ /dx x ∆E/E=0.1 χχ -> γγ χχ -> Zγ total spectrum 0.1 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 dNγ /dx x ∆E/E=0.01 χχ -> γγ χχ -> Zγ total spectrum

GAMMA400 DAMPE Fermi CTA Energy range [GeV] 0.1-3000 5-10000 0.1-300 >10 Angular res [deg] ∼0.01 0.1 at 100 GeV 0.1 0.1 Energy res [%] ∼1 ∼1 at 800 GeV 10 15

2018∼ 2015∼

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 16 / 19

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Model of Scalar Dark Matter Gamma-ray signatures

Fitting to Gamma-ray flux

53 Fermi data points are used. constraint from thermal relic density of DM : Ωh2 = 0.12 three parameters : mχ, µ, y. → one of them is fixed by Ωh2 = 0.12 → the degree of freedom is 2. mχ = 155 GeV, µ = 2.05, y = 1.82, → σvf f γ = 4.7 × 10−27 cm3/s

10-7 10-6 10-5 10-4 100 101 102 103 Eγ

2dΦγ/dEγ[GeVcm-2s-1sr-1]

Eγ[GeV] Fermidata Background VIB+FSR+Background VIB+FSR

1 2 3 4 5 6 7 8 9 100 120 140 160 180 200 220 µ mχ [GeV] Fermidata90.0%CL Fermidata68.3%CL yL=1.0 yL=1.5 yL=2.0 yL=3.0 yL=4.0

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 17 / 19

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Model of Scalar Dark Matter Constraint

Constraint from Anomalous Magnetic Moment

Experiments δae = ae(SM) − ae(exp) = 1.06 × 10−12 δaµ = aµ(SM) − aµ(exp) = 25.5 × 10−10 From Yukawa interaction δaf = y 2 (4π)2 m2

f

m2

χ

2 + 3µ − 6µ2 + µ3 + 6µ log µ 6(1 − µ)4 using the fitting parameters δae = 9.4 × 10−15, δaµ = 4.0 × 10−10 → satisfy the constraint. But, if we have the Yukawa interaction with different flavor at the same time, LFV such as µ → eγ gives a strong constraint.

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 18 / 19

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Summary

Summary

Gamma-ray signatures from DM annihilation is characteristic. In the model we considered, the annihilation cross section is dominated by d-wave. → strong gamma-ray can be emitted consistently with thermal DM prodction. Line spectrum is also important for future instruments. Strong constraint would be given from LFV. Future works Consider the other constraints? Strong ν flux via electroweak bremsstrahlung?

Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 19 / 19