Leptogenesis via Phase Transition Ye-Ling Zhou, Southampton, 27 - PowerPoint PPT Presentation

Leptogenesis via 
 Phase Transition Ye-Ling Zhou, Southampton, 27 November 2018 1. Baryogenesis via leptonic CP-violating phase transition 
 S Pascoli, J Turner, YLZ , arXiv:1609.07969 2. Leptogenesis via Varying Weinberg Operator: the Closed-Time-Path Approach, 
 J Turner, YLZ , arXiv:1808.00470 3. Leptogenesis via Varying Weinberg Operator: a Semi-Classical Approach 
 S Pascoli, J Turner, YLZ , arXiv:1808.00475

Origin of neutrino masses Why neutrinos have masses and 
 UV Completion of the these masses are so tiny? Weinberg operator In the SM without extending particle content, ν the only way to generate a neutrino mass is N using higher dimensional operators. Δ L=2 Weinberg operator L W = � αβ Λ ` α L HC ` β L H + h.c. type-I,II,III seesaw, inverse m ν = λ v 2 Λ seesaw, loop corrections, 
 λ ∼ 10 15 GeV H R-parity violation,… Λ �2

Baryon-antibaryon asymmetry Most matter is formed by baryon, not anti-baryon. n B − n B Dark Matter 26% η B ≡ n γ = (6 . 12 ± 0 . 04) × 10 − 10 Matter 5% Planck 2018 Dark Energy 69% The SM cannot provide strong out-of-equilibrium dynamics and enough CP violation. �3

Baryogenesis via leptogenesis Big Bang Seesaw scale 
 (10 14 GeV) 10 12 GeV sphaleron 
 leptogenesis 
 processes 
 in equilibrium 10 9 GeV Δ (B-L)=0 Δ L 10 6 GeV Δ B TeV scale Buchmuller EW scale GeV scale sphaleron decouple �4

Baryogenesis via leptogenesis Sakharov conditions for leptogenesis SM L/B-L violation C/CP violation Out of equilibrium dynamics �5

Leptogenesis via RH neutrinos Classical thermal leptogenesis [Fukugita, Yanagida, 1986] RH neutrino N Complex Yukawa couplings Decay of lightest N H H H   L β L β   N j   L α ∆ f ` α ∝ Im   N 1 N j N 1 L α N 1 L α   Akhmedov-Rubakov-Smirnov mechanism [9803255] Production Propagation Annihilation L α L β H H e iP i · x N i N α N β P αβ quarks, vectors in quarks, vectors in the thermal plasma the thermal plasma The SM lepton number is broken, 
 L but the “generalised” lepton number is conserved. L = L + L N �6

Leptogenesis via Weinberg operator Three Sakharov conditions are satisfied as follows: The Weinberg operator violates lepton number and leads to LNV processes in the thermal universe. SP and their CP- conjugate processes The Weinberg operator is very weak and can directly provide out of equilibrium dynamics in the early Universe. T < 10 12 GeV JT < H u ∼ 10 T 2 λ 2 m 2 ν T 3 3 3 Λ 2 T 3 ⇠ Γ W ⇠ h σ n i ⇠ v 4 (4 π ) 3 (4 π ) 3 m pl H No washout if there are no other LNV sources. We assume a cosmological phase transition, which leads to a spacetime-varying Weinberg operator, to give rise to CP violation. �7

Motivation for phase transitions A lot of symmetries have been proposed in the lepton sector. Their breaking may lead to a time-varying Weinberg operator. B-L symmetry breaking To generate a CP violation, at least two scalars are needed. Flavour & CP symmetry breaking Flavour symmetries Continuous Discrete Fraggatt-Nielson, L mu -L tau … Z n Abelian A 4 , S 4 , A 5 , Δ (48), … Non-Abelian SU(3), SO(3), … �8

Motivation for phase transitions A lot of symmetries have been proposed in the lepton sector. Their breaking may lead to a time-varying Weinberg operator. B-L symmetry breaking To generate a CP violation, at least two scalars are needed. Flavour & CP symmetry breaking ⇒ Flavour symmetries Continuous Discrete Fraggatt-Nielson, L mu -L tau … Z n Abelian A 4 , S 4 , A 5 , Δ (48), … Non-Abelian SU(3), SO(3), … Phase Transition (PT) �9

PT-induced spacetime-varying Weinberg operator Weinberg operator before PT φ i φ j φ i λ 0 λ i λ ij ` ` X X + + ij i H H Weinberg operator after PT h φ i i h φ i i h φ j i λ λ 0 λ i λ ij ` ` ` ` X X + + = ij i H H H H �10

PT-induced spacetime-varying Weinberg operator Phase I Bubble wall Phase II v w x 1 x 3 = z x 2 at a fixed point in the space λ αβ ( t ) Single-scalar case λ αβ f ( t → −∞ ) = 0 λ αβ ( x ) = λ 0 αβ + λ 1 αβ f ( x ) f ( t → + ∞ ) = 1 λ 0 αβ λ 0 αβ + λ 1 αβ ≡ λ αβ t �11

How to calculate lepton-antilepton asymmetry? In the Closed Time Path formalism. arXiv:1609.07969 , 1808.00470 The lepton asymmetry is determined to the self energy corrections including CPV source in CTP formalism × In a semi-classical approximation arXiv:1808.00475 The lepton asymmetry is obtained by the interference of the interference 
   of two Weinberg 
   αβ ( t 1 ) λ ∗ λ αβ ( t 2 ) ∆ f ` α ∝ Im operators at 
 different 
   spacetimes. �12

EOM for leptons and antileptons We treating the Higgs as a background field in the thermal bath. h H i = 0 Decoherence effect is included by replacing the incoming and outgoing momentums L : decoherence length to avoid the the interference with infinite distance di ff erence EOM of lepton propagating along the z direction is given by j z = +1 2 j z = − 1 2 Wave functions Majorana-like 
 mass matrix �13

Lepton-antilepton transition In the rest wall frame Phase I Phase II Bubble wall k in `` ( z 0 ) R ¯ k out z 0 k in z ` ( z 0 ) R ` ¯ k out z 1 = z − z 0 antilepton to lepton lepton to antilepton Asymmetry �14

Leptogenesis via Weinberg operator (in CTP approach) Asymmetry between lepton and antilepton number density 25 m ν = λ v 2 ν = λ 0 v 2 H m 0 H 20 Λ Λ Leptons and the F ( x γ , x cut ) energy/momentum transfer from Higgs are assumed x cut = 0 . 50 the bubble wall to leptons to be thermal 15 distributed. x cut = | k out | − | k in | = 1 2 T 2 Thermal masses are neglected. arXiv:1808.00470 10 γ = 6 /L The damping width 
 corresponds to decoherence at large time duration. ( γ H for Higgs, γ ` for lepton) 5 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 x γ x γ = ( γ H + γ l ) /T �15

Temperature for phase transition Big Bang Seesaw scale 
 (10 14 GeV) 10 12 GeV T ∼ 10 11 GeV leptogenesis via PT sphaleron process 
 in equilibrium 10 9 GeV 10 6 GeV n B ≈ − 1 3 n ` TeV scale EW scale sphaleron decouple ∼ (0 . 1eV) 2 Im { tr[ m 0 ν ] } ∼ m 2 ν m ∗ ν GeV scale f ` ∼ O (10 2 ) m 2 ⌫ T 2 η B v 4 H v 2 p H T ∼ O (10) ∆ f ` m ⌫ �16

Summary I introduce a novel mechanism of leptogenesis via Weinberg operator. No explicit new particles are required, but just a spacetime-varying Weinberg operator. The spacetime-varying coe ffi cient of the Weinberg operator is triggered by a phase transition. In order to generate enough baryon-antibaryon asymmetry, the temperature for phase transition should be around 10 11 GeV. Thank you very much!

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Closed Time Path (CTP) approach Propagators t 1 t 2 S T Feynman αβ ( x 1 , x 2 ) = h T [ ` α ( x 1 ) ` β ( x 2 )] i Dyson S T αβ ( x 1 , x 2 ) = h T [ ` α ( x 1 ) ` β ( x 2 )] i S < αβ ( x 1 , x 2 ) = �h ` β ( x 2 ) ` α ( x 1 ) i Wightman S > αβ ( x 1 , x 2 ) = h ` α ( x 1 ) ` β ( x 2 ) i x µ x µ 1 = ( t 1 , ~ x 1 ) 2 = ( t 2 , ~ x 2 ) Kadanoff-Baym equation /S <,> � Σ H � S <,> � Σ <,> � S H = 1 Σ > � S < � Σ < � S > ⇤ ⇥ i ∂ 2 Lepton Self energy Dispersion Collision term asymmetry correction relations S H = S T − 1 ∆ n `↵ ( x ) = − 1 2( S > + S < ) n ⇤o γ 0 ⇥ S < ↵↵ ( x, x ) + S > 2tr ↵↵ ( x, x ) CPV source Z t f Σ H = Σ T − 1 2( Σ > + Σ < ) dt 1 ∂ t 1 tr[ γ 0 S < k ( t 1 , t 1 ) + γ 0 S > ∆ f ` α ( k ) = − k ( t 1 , t 1 )] ~ ~ t i �19

Classical formalism vs CTP formalism Leptogenesis via RH neutrino decay Anisimov, Buchmuller, Drewes, Mendizabal, 1012.5821 CPV source in 
 Im + × classical formalism Self energies 
 + including CPV source 
 in CTP formalism Leptogenesis via RH neutrino oscillation Im × CPV source in 
 Self energy including CPV classical formalism source in CTP formalism �20

Influence of phase transition Multi-scalar phase transition (in the thick-wall limit) λ ( x ) = λ 0 + λ 1 f 1 ( x ) + λ 2 f 2 ( x ) e.g., Im { tr[ λ ∗ ( x 1 ) λ ( x 2 )] } = Im { tr[ λ 0 λ 1 ∗ ] } [ f 1 ( x 1 ) − f 1 ( x 2 )] + Im { tr[ λ 0 λ 2 ∗ ] } [ f 2 ( x 1 ) − f 2 ( x 2 )] +Im { tr[ λ 1 ∗ λ 2 ] } [ f 1 ( x 1 ) f 2 ( x 2 ) − f 1 ( x 2 ) f 2 ( x 1 )] Interferences of different scalar VEVs cannot be neglected. Z d 4 r r 0 M ∆ n I ` ∝ Im { tr[ λ ∗ ( x ) ∂ t λ ( x )] } time-dependent integration Z d 4 r r 3 M ∆ n II ` ∝ Im { tr[ λ ∗ ( x ) ∂ z λ ( x )] } space-dependent integration Time derivative/spatial gradient Silvia Pascoli, Jessica Turner, YLZ , in progress �21

Influence of thermal effects Z Z d 4 r r 3 M d 4 r r 0 M Thermal effects influence the time- )] } )] } and space-dependent integration. Resummed propagators of the Higgs and leptons thermal equilibrium m 2 m th , ` = Re Σ th ,H = Re Π thermal mass γ ` = Im Σ 2 Im Π γ H = thermal width 2 m th , ` 2 m th ,H By assuming thermal equilibrium in the rest frame of plasma, 
 the space-dependent integration is zero. Z is invariant under parity transformation d 4 r r 3 M = 0 ⇒ )] } M �22