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Nonequilibrium QFT Approach to Leptogenesis

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Nonequilibrium QFT Approach to Leptogenesis Nonequilibrium QFT approach to leptogenesis Tibor Frossard MPIK-Heidelberg Based on arXiv:1211.2140 in collaboration with M. Garny, A. Hohenegger, A. Kartavtsev, and D. Mitrouskas Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 1 / 19 Outline Baryogenesis Leptogenesis Boltzmann approach to leptogenesis Nonequilibrium QFT approach to leptogenesis Conclusion Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 2 / 19 Baryogenesis Baryogenesis The Laws of Nature are almost The Earth is made of the same for matter and for matter antimatter! The Sun is made of matter The Milky Way is made of matter The Universe is made of matter The Universe contains almost only matter, and no antimatter! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 3 / 19 Baryogenesis Baryon-to-photon ratio n − n ¯ η = B B ∼ 6 × 10−10 nγ tBBN ∼ 1 minute tCMB ∼ 380 000 years [astro-ph/0601514] Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 4 / 19 3 Sakharov conditions Standard Model Baryon number violation $ sphalerons C and CP violation $ chirality, CKM matrix out of equilibrium dynamics $ expanding Universe Beyond SM physics: ! Electroweak baryogenesis, Affleck-Dine baryogenesis, leptogenesis, ... Baryogenesis Sakharov conditions Two different attitudes: The Universe contains initially more particles than antiparticles ! no need to produce the asymmetry The Universe was initially matter-antimatter symmetric, and the observed asymmetry must be dynamically produced Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 5 / 19 Beyond SM physics: ! Electroweak baryogenesis, Affleck-Dine baryogenesis, leptogenesis, ... Baryogenesis Sakharov conditions Two different attitudes: The Universe contains initially more particles than antiparticles ! no need to produce the asymmetry The Universe was initially matter-antimatter symmetric, and the observed asymmetry must be dynamically produced 3 Sakharov conditions Standard Model Baryon number violation $ sphalerons C and CP violation $ chirality, CKM matrix out of equilibrium dynamics $ expanding Universe Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 5 / 19 Baryogenesis Sakharov conditions Two different attitudes: The Universe contains initially more particles than antiparticles ! no need to produce the asymmetry The Universe was initially matter-antimatter symmetric, and the observed asymmetry must be dynamically produced 3 Sakharov conditions Standard Model Baryon number violation $ sphalerons C and CP violation $ chirality, CKM matrix out of equilibrium dynamics $ expanding Universe Beyond SM physics: ! Electroweak baryogenesis, Affleck-Dine baryogenesis, leptogenesis, ... Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 5 / 19 Leptogenesis Leptogenesis Leptogenesis: particular model of baryogenesis very simple model: SM particles + n (at least 2) heavy, gauge-singlet right-handed neutrinos Ni RH neutrinos are unstable main decay channels: lepton-Higgs pair antilepton-antiHiggs pair CP violation ! decay rates are unequal in an expanding Universe ! production of lepton asymmetry EW sphaleron processes transfer part of the lepton asymmetry to the baryon sector ) Production of a net baryon asymmetry! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 6 / 19 Leptogenesis Type-I seesaw Lagrangian SM + n heavy right-handed gauge-singlet Majorana neutrinos: ¯ = 1 ¯c ¯ c ¯ ~ y ¯ ~y L =LSM + Nii@Ni − 2 Mi Ni Ni + NiNi − hαi`αφNi − hiαNiφ `α the mass matrix violates lepton number Yukawa couplings h generate the vertices gives mass to active neutrinos through the seesaw formula −1 mν = −mDM mD; where mD = vh “heavy” means O(1010 − 1013) GeV ) no hope to see these particles in future experiments Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 7 / 19 Leptogenesis Evolution of the asymmetry [hep-ph/0502169] Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 8 / 19 ) into the Boltzmann equation for the leptons and antileptons! Boltzmann approach Transition amplitudes Generation of the 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 03.12.2012 9 / 19 Boltzmann approach Transition amplitudes Generation of the 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 leptons and antileptons! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 9 / 19 Boltzmann approach Boltzmann equation Z 3 3 df` 1 X d pa d pi 4 X X = ::: ::: (2π) δ( pa − pi − p`) dt 2E` 2Ea 2Ei fa:::g;fi:::g 2 × fa ::: (1 ± fi) ::: (1 − f`) jMa+:::!i+:::+`j Z 3 3 1 X d pa d pi 4 X X − ::: ::: (2π) δ( pa + p` − pi) 2E` 2Ea 2Ei fa:::g;fi:::g 2 × fa : : : f`(1 ± fi) ::: jMa+:::+`!i+:::j + similar equation for antilepton d(f`−f`¯) In equilibrium, dt is non zero if one uses the Feynman amplitudes! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 10 / 19 Boltzmann approach Double counting problem BE equations + naive Feynman amplitudes are not consistent with the third Sakharov condition ! unstable particles as in/out-state some processes are counted twice can be solved if one neglects quantum statistical factors: (1 ± fi)(1 ± fj) ::: ! 1 substraction of the real intermediate state from the s-channel 2 M`φ!`¯φ¯ : ! so-called RIS-subtraction Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 11 / 19 Boltzmann approach First principles approach RIS-subtraction is an unsatisfactory solution derive Boltzmann-like equations from first principles ! free of double counting problem ! include thermal masses ! include thermal amplitudes ! include thermal width keep track of the approximations done ! range of validity of the resulting equations ) Nonequilibrium quantum field theory approach! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 12 / 19 Nonequilibrium QFT approach Basics of nonequilibrium QFT Lepton propagator on CTP: ¯ Sαβ(x; y) =< TC`α(x)`β(y) > Closed Time Path Schwinger-Dyson equation ^−1 ^−1 ^ δiΓ2 S (x; y) = S0 (x; y) − Σ(x; y) ; Σαβ(x; y) = − δSβα(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 03.12.2012 13 / 19 Nonequilibrium QFT approach Kadanoff-Baym equations Kadanoff-Baym equations Z x0 Z y0 ^ 4 ^ ^ 4 ^ ^ i@=xSF (x; y) = d zΣρ(x; z)SF (z; y) − d zΣF (x; z)Sρ(z; y) 0 0 Z x0 ^ 4 ^ ^ i@=xSρ(x; y) = d zΣρ(x; z)Sρ(z; y) y0 equivalent to the Schwinger-Dyson equation exact equations only Gaussian initial conditions self-energies are functional of the propagators ! need a loop expansion extremely difficult to solve numerically ! approximations needed! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 14 / 19 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 03.12.2012 15 / 19 Nonequilibrium QFT approach Results: RH neutrino decay z = M1=T 2 2 jMNi!`φj − M ¯¯ = Ni!`φ i 2 2 jMNi!`φj + MNi!`¯φ¯ h: : : γD i Ni : reaction density ∼ thermally averaged amplitudes ) thermal enhancement partially compensated by thermal masses! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 16 / 19 Nonequilibrium QFT approach Results: scattering process Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 17 / 19 Nonequilibrium QFT approach Results: Higgs decay due to thermal masses the phase space for heavy neutrino shrinks at high temperature at even higher temperature the Higgs decay becomes kinematically allowed Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 18 / 19 Thank you for your attention! Conclusion Conclusion Nonequilibrium QFT is the appropriate tool to study leptogenesis lead to consistent set of equations ! free of double counting problem ! include thermal masses ! include thermal corrections to the amplitudes total amplitudes are not very sensitive to thermal corrections ! tree level CP-violating parameter is more sensitive to thermal corrections ! loop corrections inclusion of top scattering (work in progress) inclusion of gauge scattering (more complicated . ) Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 19 / 19 Conclusion Conclusion Nonequilibrium QFT is the appropriate tool to study leptogenesis lead to consistent set of equations ! free of double counting problem ! include thermal masses ! include thermal corrections to the amplitudes total amplitudes are not very sensitive to thermal corrections ! tree level CP-violating parameter is more sensitive to thermal corrections ! loop corrections inclusion of top scattering (work in progress) inclusion of gauge scattering (more complicated . ) Thank you for your attention! Tibor Frossard (MPIK-HD) Nonequilibrium QFT in leptogenesis 03.12.2012 19 / 19.
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