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

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

Outline Outline Introduction Simple Model of Scalar Dark Matter Gamma-ray Signatures Summary Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 2 / 19

Introduction Indirect detection In particular, γ -ray can be a characteristic signal of DM. · γ -ray flux · But Fermi Co. is negative. Significance is 1 . 6 σ at 133 GeV. E 2 · dJ/dE [GeV / cm 2 / s / sr] 10 -5 10 -6 10 -7 10 0 10 1 10 2 E [GeV] Fermi Collaboration, arXiv: 1305.5597 C. Weniger, arXiv:1210.3013 This peak would be a fake, but · γ -ray excess around 130 it is still interesting to study a GeV? model which generates such a · � σ v γ � ∼ 10 − 27 cm 3 / s strong γ -ray. thermal DM ↔ 10 − 26 cm 3 / s · We need better instruments. Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 3 / 19

Introduction Gamma-ray spectrum Gamma-ray spectrum from dark matter annihilation Bringmann & Weniger � 2012 � � E � E � 0.15 10 � E � E � 0.02 ΓΓ 1 box x 2 dN � dx , , W W q q Z Z VIB 0.1 0.01 0.02 0.05 0.10 0.20 0.50 1.00 2.00 x � E � m Χ T. Bringbann, C. Weniger arXiv:1208.5481 Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 4 / 19

Introduction Gamma-ray spectrum Gamma-ray spectrum Line spectrum ex. χχ → γγ , χχ → Z γ suppression factor ∼ α 2 em Internal bremsstrahlung χχ → f f γ When chiral suppression is effective, it becomes important. suppression factor ∼ α em Box type spectrum ex. χχ → SS → 4 γ ( S : light mediator) if m χ ≫ m S , box type if m χ ≈ m S , E γ ∼ m χ / 2 Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 5 / 19

Introduction Thermal Dark Matter Thermal relic of dark matter Boltzmann equation: dn n 2 − n 2 � � dt = −� σ v � eq σ v = a + bv 2 + · · · , → � σ v � = a + b (6 T / m χ ) + · · · � σ v � th ∼ 3 × 10 − 26 cm 3 / s ↔ Relic density Ω h 2 = 0 . 12 For fermion DM, typically Internal bremsstraglung: σ v f f γ ∼ 10 − 28 cm 3 / s Monochromatic gamma: σ v γγ ∼ 10 − 30 cm 3 / s Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 6 / 19

Model of Scalar Dark Matter Model Real singlet scalar χ (DM), Z 2 = − 1 Vector like charged fermion ψ (mediator), Z 2 = − 1, Y = − 1 Interaction: L Y = y χψ P R f + h . c . φ φ † φ + m 2 2 χ 2 + λ φ � 2 + λ χ 4! χ 4 + λ χ V = m 2 � φ † φ 2 χ 2 � φ † φ � 2 φ ( x ) = � φ � + h ( x ) After φ gets VEV: √ 2 The coupling λ should be suppressed from the constraint of direct detection. σ p = c λ 2 µ 2 χ m 2 � 7 . 6 × 10 − 46 [ cm 2 ] p χ m 4 4 π m 2 h LUX Collaboration, arXiv: 1310.8214 When m p ≪ m χ , the coupling is limited as λ � 3 . 1 × 10 − 4 . Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 7 / 19

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 y 4 m 2 y 4 m 2 1 1 + 2 µ f f (1 + µ ) 4 v 2 σ v f f = (1 + µ ) 2 − 4 π m 2 m 2 6 π m 2 m 2 χ χ χ χ µ ≡ m 2 y 4 1 (1 + µ ) 4 v 4 + O ( v 6 ) , ψ + 60 π m 2 m 2 χ χ · when m f ≪ m χ , 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

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: O S ∼ χχ f f In our case, m f is multiplied to the operator. p-wave initial state: CP=odd, J = 1 J = 1 operator cannnot be constructed. ↔ χ � � � f γ µ f � O P ∼ χ∂ µ = 0 Note: p-wave exists for complex scalar DM. Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 9 / 19

Model of Scalar Dark Matter d-wave initial state: CP=even, J = 2 corresponding effective operator O D ∼ ∂ µ χ∂ ν χ T 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

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 → Z γ 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

Model of Scalar Dark Matter Gamma-ray signatures Internal bremsstrahlung · differential cross section α em y 4 d σ v f f γ � 2 x x = (1 − x ) ( µ + 1)( µ + 1 − 2 x ) − 4 π 2 m 2 ( µ + 1 − x ) 2 dx χ − ( µ + 1)( µ + 1 − 2 x ) � µ + 1 �� x ≡ E γ log , 2( µ + 1 − x ) 3 µ + 1 − 2 x m χ 10 1 µ + µ − ( γ ) · When µ � 4, a sharp peak appears τ + τ − ( γ ) 10 0 ¯ bb ( γ,g ) around E γ ∼ m χ x 2 dN/dx 10 -1 · � σ v f f γ � ∼ 10 − 27 cm 3 / s 10 -2 10 -3 T. Bringmann et al., arXiv:1203.1312 10 -2 10 -1 10 0 x = E/m χ Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 12 / 19

Model of Scalar Dark Matter Gamma-ray signatures Line spectrum χχ → γγ comes from box diagrams χ γ χ γ χ γ f ψ f ψ f f ψ ψ f ψ f ψ χ γ χ γ χ γ χχ → Z γ Z γ is related with γγ � 3 m 2 � 1 − 1 � σ v Z γ � ≈ 2 tan 2 θ W Z � σ v γγ � 4 m 2 χ The cross sections are typically σ v γγ ≈ σ v Z γ ≈ 10 − 28 or 10 − 29 cm 3 / s when m χ � 1000 GeV . Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 13 / 19

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: p 1 = p 2 = ( m χ , 0 ) ≡ p , Final state: k 1 , k 2 Flow of calculation G. Bertone et al. arXiv:0904.1442 1 In general, i M is decomposed as M µν = p µ p ν A + k µ 1 B + k µ 1 k ν 2 k ν 2 C + · · · + g µν A loop where i M = i ǫ ∗ µ ( k 1 ) ǫ ∗ ν ( k 2 ) M µν . only A loop remains. 2 Simplify A loop by Passarino-Veltman reduction 3 cross section: σ v = α 2 em α 2 y |A loop ( µ ) | 2 2 π m 2 χ Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 14 / 19

Model of Scalar Dark Matter Gamma-ray signatures � 1 � µ − 1 � � − 2 µ Arcsin 2 µ = m 2 ψ / m 2 A loop = 2 − 2 log √ µ , χ > 1 µ S. Tulin et al. arXiv:1208.0009 The behavior is not good at µ ∼ 1. divergence 8 Ref. result Our result 6 4 A loop 2 0 -2 1 1.5 2 2.5 3 3.5 4 µ Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 15 / 19

Model of Scalar Dark Matter Gamma-ray signatures Energy spectrum χχ -> γγ χχ -> γγ χχ -> Z γ χχ -> Z γ total spectrum total spectrum ∆ E/E=0.1 ∆ E/E=0.01 1 1 dN γ /dx dN γ /dx 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 x x 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

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 : Ω h 2 = 0 . 12 three parameters : m χ , µ , y . → one of them is fixed by Ω h 2 = 0 . 12 → the degree of freedom is 2. m χ = 155 GeV , µ = 2 . 05 , y = 1 . 82 , → � σ v f f γ � = 4 . 7 × 10 − 27 cm 3 / s 10 -4 9 Fermi�data�90.0%CL Fermi�data Fermi�data�68.3%CL 2 d Φ γ /dE γ � [GeVcm -2 s -1 sr -1 ] Background 8 y L =1.0 VIB+FSR+Background y L =1.5 VIB+FSR 7 y L =2.0 10 -5 y L =3.0 y L =4.0 6 µ 5 10 -6 4 3 E γ 2 10 -7 1 10 0 10 1 10 2 10 3 100 120 140 160 180 200 220 E γ �[GeV] m χ [GeV] Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 17 / 19

Model of Scalar Dark Matter Constraint Constraint from Anomalous Magnetic Moment Experiments δ a e = a e ( SM ) − a e ( exp ) = 1 . 06 × 10 − 12 δ a µ = a µ ( SM ) − a µ ( exp ) = 25 . 5 × 10 − 10 From Yukawa interaction 2 + 3 µ − 6 µ 2 + µ 3 + 6 µ log µ y 2 m 2 f δ a f = (4 π ) 2 m 2 6(1 − µ ) 4 χ using the fitting parameters δ a e = 9 . 4 × 10 − 15 , δ a µ = 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 → e γ gives a strong constraint. Takashi Toma (IPPP) BURI 2014 14th Feb. 2014 18 / 19