Nonequilibrium QFT approach to leptogenesis Tibor Frossard MPIK-Heidelberg In collaboration with M. Garny, A. Hohenegger, A. Kartavtsev, and D. Mitrouskas Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 1 / 11 1 B + L violating sphalerons + L violating Majorana mass 2 Yukawa coupling hαi 3 Expanding Universe + Ni decay Leptogenesis SM + 3 heavy Majorana neutrinos: Dynamical generation of the 1 L =LSM + N¯i i@= − Mi Ni baryon asymmetry: 2 ¯ ~ y ¯ ~y ! 3 Sakharov conditions: − hαi`αφPRNi − hiαNiφ PL`α 1 Baryon number violation 2 C and CP violation 3 Out of equilibrium dynamics ) Need physic beyond the SM Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 nγ Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 1 B + L violating sphalerons + L violating Majorana mass 2 Yukawa coupling hαi 3 Expanding Universe + Ni decay Leptogenesis SM + 3 heavy Majorana neutrinos: 1 ¯ = L =LSM + 2 Ni i@ − Mi Ni ¯ ~ y ¯ ~y − hαi`αφPRNi − hiαNiφ PL`α ) Need physic beyond the SM Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 nγ Dynamical generation of the baryon asymmetry: ! 3 Sakharov conditions: 1 Baryon number violation 2 C and CP violation 3 Out of equilibrium dynamics Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 1 B + L violating sphalerons + L violating Majorana mass 2 Yukawa coupling hαi 3 Expanding Universe + Ni decay Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 Leptogenesis nγ SM + 3 heavy Majorana neutrinos: Dynamical generation of the 1 L =LSM + N¯i i@= − Mi Ni baryon asymmetry: 2 ¯ ~ y ¯ ~y ! 3 Sakharov conditions: − hαi`αφPRNi − hiαNiφ PL`α 1 Baryon number violation 2 C and CP violation 3 Out of equilibrium dynamics ) Need physic beyond the SM Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 2 Yukawa coupling hαi 3 Expanding Universe + Ni decay Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 Leptogenesis nγ SM + 3 heavy Majorana neutrinos: Dynamical generation of the 1 L =LSM + N¯i i@= − Mi Ni baryon asymmetry: 2 ¯ ~ y ¯ ~y ! 3 Sakharov conditions: − hαi`αφPRNi − hiαNiφ PL`α 1 Baryon number violation 1 B + L violating sphalerons+ 2 C and CP violation L violating Majorana mass 3 Out of equilibrium dynamics ) Need physic beyond the SM Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 3 Expanding Universe + Ni decay Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 Leptogenesis nγ SM + 3 heavy Majorana neutrinos: Dynamical generation of the 1 L =LSM + N¯i i@= − Mi Ni baryon asymmetry: 2 ¯ ~ y ¯ ~y ! 3 Sakharov conditions: − hαi`αφPRNi − hiαNiφ PL`α 1 Baryon number violation 1 B + L violating sphalerons + 2 C and CP violation L violating Majorana mass 3 Out of equilibrium dynamics 2 Yukawa coupling hαi ) Need physic beyond the SM Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 Leptogenesis Baryogenesis via Leptogenesis Matter-antimatter asymmetry in the Universe CMB + BBN ) n − n ¯ η = B B = (6:2 ± 0:2) 10−10 Leptogenesis nγ SM + 3 heavy Majorana neutrinos: Dynamical generation of the 1 L =LSM + N¯i i@= − Mi Ni baryon asymmetry: 2 ¯ ~ y ¯ ~y ! 3 Sakharov conditions: − hαi`αφPRNi − hiαNiφ PL`α 1 Baryon number violation 1 B + L violating sphalerons + 2 C and CP violation L violating Majorana mass 3 Out of equilibrium dynamics 2 Yukawa coupling hαi ) Need physic beyond the 3 Expanding Universe + N SM i decay Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 2 / 11 ) into the Boltzmann equation for the lepton number! Leptogenesis Canonical approach Generation of an asymmetry: production washout 4 2 Ni (inverse)decay O h O h ∆L = 2 scattering O h6 O h4 2 4 2 2 top scattering O λt h O λt h gauge scattering O g2h4 O g2h2 Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 3 / 11 ) into the Boltzmann equation for the lepton number! Leptogenesis Canonical approach Generation of an asymmetry: production washout 4 2 Ni (inverse)decay O h O h ∆L = 2 scattering O h6 O h4 2 4 2 2 top scattering O λt h O λt h gauge scattering O g2h4 O g2h2 Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 3 / 11 Leptogenesis Canonical approach Generation of an asymmetry: production washout 4 2 Ni (inverse)decay O h O h ∆L = 2 scattering O h6 O h4 2 4 2 2 top scattering O λt h O λt h gauge scattering O g2h4 O g2h2 ) into the Boltzmann equation for the lepton number! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 3 / 11 Vacuum amplitudes in the hot Universe ! thermal masses? ! thermal decay width? ! thermal amplitudes? Nonequilibrium Quantum Field Theory approach is needed!! Leptogenesis Canonical approach This approach suffers from several problems: Double counting problem ! can be solved if one neglects the quantum statistical factors ) Real intermediate state substraction Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 4 / 11 Nonequilibrium Quantum Field Theory approach is needed!! Leptogenesis Canonical approach This approach suffers from several problems: Double counting problem ! can be solved if one neglects the quantum statistical factors ) Real intermediate state substraction Vacuum amplitudes in the hot Universe ! thermal masses? ! thermal decay width? ! thermal amplitudes? Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 4 / 11 Leptogenesis Canonical approach This approach suffers from several problems: Double counting problem ! can be solved if one neglects the quantum statistical factors ) Real intermediate state substraction Vacuum amplitudes in the hot Universe ! thermal masses? ! thermal decay width? ! thermal amplitudes? Nonequilibrium Quantum Field Theory approach is needed!! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 4 / 11 Schwinger-Dyson equation ^−1 ^−1 ^ αβ δiΓ2 S (x; y) = S0 (x; y) − Σ(x; y) ; Σij (x; y) = − βα δSji (y; x) 2PI effective Γ = = 2 action ^ ^ i 0 0 ^ ! doubling of the d.o.f.: S(x; y) = SF (x; y) − 2 signC(x − y ) Sρ(x; y) | {z } | {z } statistical spectral Nonequilibrium QFT approach Basics of nonequilibrium QFT Right-handed neutrinos propagator on CTP: αβ α ¯ β Sij (x; y) =< TCNi (x)Nj (y) > Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 5 / 11 ^ ^ i 0 0 ^ ! doubling of the d.o.f.: S(x; y) = SF (x; y) − 2 signC(x − y ) Sρ(x; y) | {z } | {z } statistical spectral Nonequilibrium QFT approach Basics of nonequilibrium QFT Right-handed neutrinos propagator on CTP: αβ α ¯ β Sij (x; y) =< TCNi (x)Nj (y) > Schwinger-Dyson equation ^−1 ^−1 ^ αβ δiΓ2 S (x; y) = S0 (x; y) − Σ(x; y) ; Σij (x; y) = − βα δSji (y; x) 2PI effective Γ = = 2 action Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 5 / 11 Nonequilibrium QFT approach Basics of nonequilibrium QFT Right-handed neutrinos propagator on CTP: αβ α ¯ β Sij (x; y) =< TCNi (x)Nj (y) > Schwinger-Dyson equation ^−1 ^−1 ^ αβ δiΓ2 S (x; y) = S0 (x; y) − Σ(x; y) ; Σij (x; y) = − βα δSji (y; x) 2PI effective Γ = = 2 action ^ ^ i 0 0 ^ ! doubling of the d.o.f.: S(x; y) = SF (x; y) − 2 signC(x − y ) Sρ(x; y) | {z } | {z } statistical spectral Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 5 / 11 Quantum Boltzmann equation Z 4 d d p h p p i (n`(t)−n`¯(t)) = gw 4 tr Σ`<(t; p)(1 − f` ) + Σ`>(t; p)f` S`ρ(t; p) dt (2π) | {z } | {z } gain term loss term Σ` = Nonequilibrium QFT approach Quantum Boltzmann equation Wigner transform $ Fourrier transform wrt relative coordinates Gradient expansion $ Expansion in slow relative to fast time-scales (H=T ) Quasiparticle approximation $ Narrow width approximation Kadanoff-Baym ansatz $ One-particle distribution function Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 6 / 11 Nonequilibrium QFT approach Quantum Boltzmann equation Wigner transform $ Fourrier transform wrt relative coordinates Gradient expansion $ Expansion in slow relative to fast time-scales (H=T ) Quasiparticle approximation $ Narrow width approximation Kadanoff-Baym ansatz $ One-particle distribution function Quantum Boltzmann equation Z 4 d d p h p p i (n`(t)−n`¯(t)) = gw 4 tr Σ`<(t; p)(1 − f` ) + Σ`>(t; p)f` S`ρ(t; p) dt (2π) | {z } | {z } gain term loss term Σ` = Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 6 / 11 - neglect the off-diagonal components The amplitudes incorporate thermal masses and thermal widths but, ! Self-energy contribution to the decay rate is missing! ! s × s and t × t channels of the scattering processes are missing! ) need to go beyond the free propagator approximation! Nonequilibrium QFT approach Lepton asymmetry Free (thermal-) propagators into the lepton self-energy: 1 p 0 2 2 1 k 0 2 2 S`F = ( 2 − f` )PLp=sign(p )(2π)δ(p − m` ) ∆φF = ( 2 + fφ )sgn(k )(2π)δ(k − mφ) ij ij 1 q 0 2 2 S = δ ( − f )(q + Mi)sign(q )(2π)δ(q − M ) NF 2 Ni = i Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 27.09.2012 7 / 11 - neglect the off-diagonal components The amplitudes incorporate thermal masses and thermal widths but, ! Self-energy contribution to the decay rate is missing! ! s × s and