A WIMPy Leptogenesis Miracle Baryogenesis via WIMP freeze-out Brian Shuve with Yanou Cui and Lisa Randall Harvard University SUSY 2011 August 31, 2011
Outline Motivation Overview of WIMPy baryogenesis Toy model of WIMPy leptogenesis Detection possibilities B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 2 / 23
Motivation There is a remarkable coincidence between the dark matter and baryon densities Ω DM ≈ 5 Ω baryon Traditional models of WIMP dark matter do not address this coincidence ◮ Dark matter is a thermal relic ◮ Relic density set by annihilation cross section: WIMP miracle DM SM 1 n DM ∝ s σ ann DM SM B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 3 / 23
Motivation Nearly all models explaining the DM-baryon ratio use asymmetric dark matter Compelling scenario with many possible mechanisms and models ◮ Transfer of the B asymmetry to dark matter ◮ Transfer of a dark matter asymmetry to B ◮ Co–generation of the asymmetries New work: transfer by mass mixing (see arXiv:1106.4834 and Yanou’s talk) B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 4 / 23
Motivation Nearly all models explaining the DM-baryon ratio use asymmetric dark matter Compelling scenario with many possible mechanisms and models ◮ Transfer of the B asymmetry to dark matter ◮ Transfer of a dark matter asymmetry to B ◮ Co–generation of the asymmetries New work: transfer by mass mixing (see arXiv:1106.4834 and Yanou’s talk) (For more info, see SPIRES: “find t asymmetric dark matter”and references cited therein) B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 4 / 23
Motivation Nearly all models explaining the DM-baryon ratio use asymmetric dark matter Compelling scenario with many possible mechanisms and models ◮ Transfer of the B asymmetry to dark matter ◮ Transfer of a dark matter asymmetry to B ◮ Co–generation of the asymmetries New work: transfer by mass mixing (see arXiv:1106.4834 and Yanou’s talk) (For more info, see SPIRES: “find t asymmetric dark matter”and references cited therein) However, asymmetric dark matter models give up the WIMP miracle . B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 4 / 23
WIMPy baryogenesis We present a model of symmetric DM that preserves the WIMP miracle and gives a connection between the DM and baryon densities. WIMPy baryogenesis: WIMP dark matter annihilates through baryon-violating couplings Physical CP phases in annihilation operators Out-of-equilibrium condition satisfied by WIMP freeze-out WIMP freeze-out can generate a baryon asymmetry! Also, baryogenesis is around the weak scale ⇒ new charged states and CP -phases Asymmetry generation through annihilation first proposed by Gu and Sarkar, 2009 For another way of connecting the WIMP miracle and baryon density, see McDonald, 1009.3227 and 1108.4653 B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 5 / 23
Overview of WIMPy baryogenesis Baryon asymmetry comes from interference of tree-level and loop annihilation diagrams: DM B DM B DM B B B B DM DM DM The baryon-violating coupling also leads to washout processes: ¯ B B B ¯ B B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 6 / 23
Overview of WIMPy baryogenesis: evolution Consider dark matter particle X Boltzmann equations: In terms of Y i = n i / s and x = m X / T , the evolution is schematically: dY X X − ( Y eq � Y 2 X ) 2 � = − A � σ ann v � + back − reaction dx dY ∆ B Y 2 X − ( Y eq X ) 2 � � Y eq � = ǫ A � σ ann v � − C � σ washout v � Y ∆ B i dx i ǫ = fractional asymmetry produced per annihilation A and C are coefficient functions including factors of s , H , . . . Y i are other baryon-number-carrying fields B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 7 / 23
Overview of WIMPy baryogenesis: asymmetry In the limit where back-reaction on X is small, � x � x � � dx ′ dY X ( x ′ ) x ′ dx ′′ C � σ washout v � � Y eq ( x ′′ ) Y ∆ B ( x ) ≈ − ǫ exp − i dx ′ 0 i Approximate exp( · · · ) ≈ θ ( x − x 0 ), where x 0 is the time of washout freeze-out: Y ∆ B ( x ) ≈ ǫ [ Y X ( x 0 ) − Y X ( x )] θ ( x − x 0 ) B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 8 / 23
Overview of WIMPy baryogenesis: asymmetry In the limit where back-reaction on X is small, � x � x � � dx ′ dY X ( x ′ ) x ′ dx ′′ C � σ washout v � � Y eq ( x ′′ ) Y ∆ B ( x ) ≈ − ǫ exp − i dx ′ 0 i Approximate exp( · · · ) ≈ θ ( x − x 0 ), where x 0 is the time of washout freeze-out: Y ∆ B ( x ) ≈ ǫ [ Y X ( x 0 ) − Y X ( x )] θ ( x − x 0 ) Asymmetry proportional to change in X density after washout processes freeze out B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 8 / 23
Overview of WIMPy baryogenesis: asymmetry Y ∆ B ( x ) ≈ ǫ [ Y X ( x 0 ) − Y X ( x )] θ ( x − x 0 ) 10 � 7 10 � 10 Y X 10 � 13 Y X Washout must freeze out 10 � 16 before annihilations Y X eq 10 � 19 10 � 22 15 20 25 30 35 40 45 50 x Y ∆ B ∼ 10 − 10 and ǫ < 1 ⇒ x 0 � 20 Two possibilities for successful baryogenesis: B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 9 / 23
Overview of WIMPy baryogenesis: asymmetry Y ∆ B ( x ) ≈ ǫ [ Y X ( x 0 ) − Y X ( x )] θ ( x − x 0 ) 10 � 7 10 � 10 Y X 10 � 13 Y X Washout must freeze out 10 � 16 before annihilations Y X eq 10 � 19 10 � 22 15 20 25 30 35 40 45 50 x Y ∆ B ∼ 10 − 10 and ǫ < 1 ⇒ x 0 � 20 Two possibilities for successful baryogenesis: σ ann ≫ σ washout 1 B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 9 / 23
Overview of WIMPy baryogenesis: asymmetry Y ∆ B ( x ) ≈ ǫ [ Y X ( x 0 ) − Y X ( x )] θ ( x − x 0 ) 10 � 7 10 � 10 Y X 10 � 13 Y X Washout must freeze out 10 � 16 before annihilations Y X eq 10 � 19 10 � 22 15 20 25 30 35 40 45 50 x Y ∆ B ∼ 10 − 10 and ǫ < 1 ⇒ x 0 � 20 Two possibilities for successful baryogenesis: σ ann ≫ σ washout 1 Heavy baryon states so that washout rate is Boltzmann suppressed 2 B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 9 / 23
Toy model: WIMPy leptogenesis Toy model of annihilation to leptons : Vectorlike dark matter X , ¯ X Heavy pseudoscalars S i (at least 2 needed for physical CP phase) Dark matter annihilates to Standard Model LH lepton doublet L j Vectorlike exotic lepton doublet ψ j , ¯ ψ j (with lepton flavor charge) L ⊃ L mass − i y Xi X 2 + y ′ Xi ¯ X 2 � � S i − i y L ij S i L j ψ j + h . c . 2 Lepton asymmetry converted to baryon asymmetry by sphalerons B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 10 / 23
Toy model: WIMPy leptogenesis Toy model of annihilation to leptons : Vectorlike dark matter X , ¯ X Heavy pseudoscalars S i (at least 2 needed for physical CP phase) Dark matter annihilates to Standard Model LH lepton doublet L j Vectorlike exotic lepton doublet ψ j , ¯ ψ j (with lepton flavor charge) L ⊃ L mass − i y Xi X 2 + y ′ Xi ¯ X 2 � � S i − i y L ij S i L j ψ j + h . c . 2 Lepton asymmetry converted to baryon asymmetry by sphalerons σ ann ∼ y 2 X y 2 σ washout ∼ y 4 L L B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 10 / 23
Toy model: WIMPy leptogenesis L ⊃ L mass − i y Xi X 2 + y ′ Xi ¯ X 2 � � S i − i y L ij S i L j ψ j + h . c . 2 In this model, ψ carries generalized lepton number − 1 ψ decays to sterile sector with separately conserved global symmetry, asymmetry in sterile sector equal and opposite to SM lepton asymmetry ex. gauge singlet fermion n L ⊃ y n ψ H † n B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 11 / 23
Toy model: WIMPy leptogenesis Z 4 symmetry: X and n stable Prevent L − ¯ ψ mixing Z 4 X i ¯ X − i S − 1 ψ − 1 ¯ ψ − 1 n − 1 SM fields +1 B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 12 / 23
Toy model: asymmetry generation processes Dark matter annihilations: ψ ψ † X X X L X L † Decays and inverse decays: ψ ψ † S S L L † B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 13 / 23
Toy model: asymmetry generation processes Dark matter annihilations: ψ ψ † X X X L X L † Decays and inverse decays: ψ ψ † S S L L † For weak scale masses and couplings, Γ S ≫ H and asymmetry from decays is negligible B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 13 / 23
Toy model: washout processes Washout processes: ψ ψ ψ † L † L ψ † L L † X X ψ † L L ψ † L ψ † B. Shuve (Harvard) A WIMPy Leptogenesis Miracle SUSY 2011 August 31, 2011 14 / 23
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