Transport Theory for EW Baryogenesis & Leptogenesis M.J. Ramsey-Musolf Wisconsin-Madison U Mass-Amherst Amherst Center for Fundamental Interactions Snowmass CSS, August 2013 1
Key Points • Robust tests of low-scale baryogenesis scenarios ! Refine theoretical machinery for computing asymmetries in out-of-equilibrium contexts • Pioneering work utilized conventional Boltzmann framework • Recent advances exploiting Schwinger- Keldysh/CTP formulation are providing a more systematic treatment • Considerable room for future theoretical progress exists 2
Transport Issues • How robustly can one predict charge asymmetries ( n left, Y l , Y X …) ? • CPV sources in EWB (MSSM…) • CPV decays in leptogenesis (soft lepto) • What is the role of CP-conserving dynamics ? • Particle number changing rxns in EWB • Washout in leptogenesis, asym DM… 3
Outline I. Transport dynamics in CTP II. CPV sources in EWB & soft Leptogenesis III. Particle number changing reactions in EWB IV. Flavored CPV & EWB 4
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann CTP or Schwinger-Keldysh Green’s functions % ( * ( y ) # ab = G t ( x , y ) $ G < ( x , y ) ˜ G ( x , y ) = P " a ( x ) " b ' * $ G t ( x , y ) G > ( x , y ) & ) • Appropriate for evolution of “in-in” matrix elements • Contain full info on number densities: n αβ ~ ~ • Matrices in flavor space: (e, µ , τ ) , ( t L, t R ), … 5
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann CTP or Schwinger-Keldysh Green’s functions % ( * ( y ) # ab = G t ( x , y ) $ G < ( x , y ) ˜ G ( x , y ) = P " a ( x ) " b ' * $ G t ( x , y ) G > ( x , y ) & ) • Appropriate for evolution of “in-in” matrix elements • Contain full info on number densities: n αβ ~ ~ • Matrices in flavor space: (e, µ , τ ) , ( t L, t R ), … ˜ " +… ˜ ˜ ˜ ˜ 0 0 0 G G G G = + + 6
Systematic Baryo/leptogenesis: Scale Hierarchies ! power counting EW Baryogenesis Leptogenesis Gradient expansion Gradient expansion ε w = v w (k w / ω ) << 1 ε LNV = Γ LNV / Γ Η < 1 Quasiparticle description Quasiparticle description ε p = Γ p / ω << 1 ε p = Γ p / ω << 1 Thermal, but not too dissipative Thermal, but not too dissipative ε coll = Γ coll / ω << 1 ε coll = Γ coll / ω << 1 Plural, but not too flavored ε osc = Δω / T << 1 7
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: Lowest non-trivial order in grad’s 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) 8
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) Diagonal after rotation to local mass basis: M 2 X ( ) = U + m 2 X ( ) U ~ ~ ~ ~ ( ) = U + # µ U ( t L, t R ) ! ( t 1, t 2 ) " µ X 9
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) Flavor oscillations: flavor off-diag densities 10
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) CPV in m 2 (X): for EWB, arises from spacetime varying complex phase(s) generated by interaction of background field(s) (Higgs vevs) with quantum fields 11
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) CPV in m 2 (X): for EWB, arises from spacetime varying complex phase(s) generated by interaction of background field(s) (Higgs vevs) with quantum fields How large is CPV source ? Riotto; Carena et al; Prokopec et al; Cline et al; Konstandin et al; Cirigliano et al; Kainulainen…. 12
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) CPV in m 2 (X): for EWB, arises from spacetime ✔ varying complex phase(s) generated by interaction of background field(s) (Higgs vevs) with quantum fields Resonant enhancement of CPV sources for small ε osc ✔ = recent progress Cirigliano et al 13
CPV Sources: EW Baryogenesis CPV Sources: how large a sin φ CPV necessary ? Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) VEV insert approx Resummed vevs Resummed vevs • Riotto • Konstandin, • Cirigliano et al Prokpec, Schmidt • Carena et al • Cirigliano et al Large resonant Small resonant Exact solution in two- enhancement but effect but neglected flavor toy model: not realistic in diffusion and off- large resonant small ε osc regime diag Σ ii G ij terms enhancement 14
CPV Sources: EW Baryogenesis CPV Sources: how large a sin φ CPV necessary ? Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) VEV insert approx Resummed vevs Resummed vevs • Riotto • Konstandin, • Cirigliano et al Prokpec, Schmidt • Carena et al • Cirigliano et al Large resonant Small resonant Exact solution in two- enhancement but effect but neglected flavor toy model: not realistic in diffusion and off- large resonant small ε osc regime diag Σ ii G ij terms enhancement 15
CPV Sources: EW Baryogenesis CPV Sources: how large a sin φ CPV necessary ? Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) VEV insert approx Resummed vevs Resummed vevs • Riotto • Konstandin, • Cirigliano et al Prokpec, Schmidt • Carena et al • Cirigliano et al Large resonant Small resonant Exact solution in two- enhancement but effect but neglected flavor toy model: not realistic in diffusion and off- large resonant small ε osc regime diag Σ ii G ij terms enhancement 16
CPV Sources: EW Baryogenesis CPV Sources: how large a sin φ CPV necessary ? Neglect o-d Σ ii G ij Kinetic eq (approx) in Wigner space: terms & approx Λ 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( Full ( ) ( ) ( ) solution VEV insert approx Resummed vevs Resummed vevs • Riotto • Konstandin, • Cirigliano et al Prokpec, Schmidt • Carena et al • Cirigliano et al Large resonant Small resonant Exact solution in two- enhancement but effect but neglected flavor toy model: not realistic in diffusion and off- large resonant small ε osc regime diag Σ ii G ij terms enhancement 17
CPV Sources: EW Baryogenesis CPV Sources: how large a sin φ CPV necessary ? Neglect o-d Σ ii G ij Kinetic eq (approx) in Wigner space: terms & approx Λ 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( Full ( ) ( ) ( ) solution Next steps: 1. Apply to realistic model (MSSM) VEV insert approx Resummed vevs Resummed vevs 2. Fermions • Riotto • Konstandin, • Cirigliano et al Prokpec, Schmidt • Carena et al • Cirigliano et al Large resonant Small resonant Exact solution in two- enhancement but effect but neglected flavor toy model: not realistic in diffusion and off- large resonant small ε osc regime diag Σ ii G ij terms enhancement 18
Systematic Baryo/leptogenesis: Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) Leptogenesis CPV decays Washout Flavor sensitive rxns Gauge interactions 19
CPV Asymmetries: Soft Leptogenesis Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) Soft Leptogenesis 0901.0008,1009.0003, 1107.5312 Sizeable Y l with TeV scale dof: Including finite-T statistics for external Interesting states in Boltzmann equations phenomenology ? 20
CPV Asymmetries: Soft Leptogenesis Formalism: Kadanoff-Baym to Boltzmann Kinetic eq (approx) in Wigner space: 2 k " # X G < k , X ) = $ i M 2 X ( ) , G < k , X ] $ 2 k " % , G < k , X [ [ ] + & G k , X [ ] ( ( ) ( ) ( ) Soft Leptogenesis 1307.0524, Garbrecht & MR-M Vanishing Y l : canceling contributions when stat’s included on all lines 21
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