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

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

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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

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SLIDE 1 Ye-Ling Zhou, Southampton, 27 November 2018

Leptogenesis via 
 Phase Transition

  • 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
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SLIDE 2

Origin of neutrino masses

2 In the SM without extending particle content, the only way to generate a neutrino mass is using higher dimensional operators. LW = αβ Λ `αLHC`βLH + h.c. Weinberg operator mν = λv2 H Λ Λ λ ∼ 1015 GeV ΔL=2 Why neutrinos have masses and 
 these masses are so tiny? UV Completion of the Weinberg operator N ν type-I,II,III seesaw, inverse seesaw, loop corrections, 
 R-parity violation,…
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SLIDE 3

Baryon-antibaryon asymmetry

3 Dark Energy 69% Dark Matter 26% Matter 5% nB − nB nγ ηB ≡ Planck 2018 Most matter is formed by baryon, not anti-baryon. The SM cannot provide strong out-of-equilibrium dynamics and enough CP violation. = (6.12 ± 0.04) × 10−10
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SLIDE 4 EW scale Big Bang TeV scale GeV scale 1012 GeV sphaleron decouple Seesaw scale 
 (1014 GeV) 109 GeV 106 GeV 4

Baryogenesis via leptogenesis

ΔB ΔL leptogenesis
 sphaleron 
 processes
 in equilibrium Buchmuller Δ(B-L)=0
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SLIDE 5

Baryogenesis via leptogenesis

5 Sakharov conditions for leptogenesis Out of equilibrium dynamics SM L/B-L violation C/CP violation
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SLIDE 6

Leptogenesis via RH neutrinos

6 Classical thermal leptogenesis Decay of lightest N RH neutrino N The SM lepton number is broken, 
 but the “generalised” lepton number is conserved. Complex Yukawa couplings [Fukugita, Yanagida, 1986] N1 N1 N1       Im     ∆f`α ∝ Nj Nj H H H Lα Lα Lα Lβ Lβ Pαβ Production Propagation Annihilation H Lα H Lβ eiPi·xNi Nα Nβ quarks, vectors in the thermal plasma quarks, vectors in the thermal plasma Akhmedov-Rubakov-Smirnov mechanism [9803255] L = L + LN L
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SLIDE 7

Leptogenesis via Weinberg operator

7 Three Sakharov conditions are satisfied as follows: SP The Weinberg operator violates lepton number and leads to LNV processes in the thermal universe. The Weinberg operator is very weak and can directly provide out of equilibrium dynamics in the early Universe. We assume a cosmological phase transition, which leads to a spacetime-varying Weinberg operator, to give rise to CP violation. JT ΓW Hu ∼ 10 T 2 mpl

<

T < 1012 GeV No washout if there are no other LNV sources. and their CP- conjugate processes ⇠ hσni ⇠ 3 (4π)3 λ2 Λ2 T 3 ⇠ 3 (4π)3 m2 νT 3 v4 H
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SLIDE 8

Motivation for phase transitions

B-L symmetry breaking 8 To generate a CP violation, at least two scalars are needed. Flavour & CP symmetry breaking Continuous Discrete Abelian Fraggatt-Nielson, Lmu-Ltau … Zn Non-Abelian SU(3), SO(3), … A4, S4, A5, Δ(48), … Flavour symmetries A lot of symmetries have been proposed in the lepton sector. Their breaking may lead to a time-varying Weinberg operator.
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SLIDE 9

Motivation for phase transitions

B-L symmetry breaking 9 Flavour & CP symmetry breaking To generate a CP violation, at least two scalars are needed. A lot of symmetries have been proposed in the lepton sector. Their breaking may lead to a time-varying Weinberg operator. Continuous Discrete Abelian Fraggatt-Nielson, Lmu-Ltau … Zn Non-Abelian SU(3), SO(3), … A4, S4, A5, Δ(48), … Flavour symmetries

⇒

Phase Transition (PT)

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SLIDE 10 PT-induced spacetime-varying Weinberg operator 10 Weinberg operator before PT Weinberg operator after PT φi φi φj ` ` H H λ0 λi λij + X i + X ij ` ` H H λ0 λi λij + X i + X ij hφii hφii hφji ` ` H H λ =
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SLIDE 11 x1 x2 vw x3 = z Phase I Phase II Bubble wall PT-induced spacetime-varying Weinberg operator 11 λαβ(t) λαβ λ0 αβ at a fixed point in the space f(t → −∞) = 0 f(t → +∞) = 1 Single-scalar case λ0 αβ + λ1 αβ ≡ λαβ λαβ(x) = λ0 αβ + λ1 αβf(x) t
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SLIDE 12 How to calculate lepton-antilepton asymmetry? 12 × In the Closed Time Path formalism. The lepton asymmetry is determined to the self energy corrections including CPV source in CTP formalism arXiv:1609.07969, 1808.00470 In a semi-classical approximation The lepton asymmetry is obtained by the interference of the interference 

  • f two Weinberg 

  • perators at 

different 
 spacetimes.       Im ∆f`α ∝ λ∗ αβ(t1) λαβ(t2) arXiv:1808.00475
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SLIDE 13 EOM for leptons and antileptons 13 We treating the Higgs as a background field in the thermal bath. Majorana-like
 mass matrix Wave functions EOM of lepton propagating along the z direction is given by jz = +1 2 jz = −1 2 Decoherence effect is included by replacing the incoming and
  • utgoing momentums
hHi = 0 L: decoherence length to avoid the the interference with infinite distance difference
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SLIDE 14

Lepton-antilepton transition

14 Phase I Phase II z z0 R¯ ``(z0) kout kin In the rest wall frame Bubble wall z1 = z − z0 lepton to antilepton antilepton to lepton R`¯ `(z0) kin kout Asymmetry
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SLIDE 15 0.0 0.1 0.2 0.3 0.4 0.5 xγ 5 10 15 20 25 F(xγ, xcut) xcut = 0.50 Leptogenesis via Weinberg operator (in CTP approach) 15 Leptons and the Higgs are assumed to be thermal distributed. m0 ν = λ0 v2 H Λ mν = λv2 H Λ xγ = (γH + γl)/T arXiv:1808.00470 The damping width 
 corresponds to decoherence at large time duration. γ = 6/L Asymmetry between lepton and antilepton number density (γH for Higgs, γ` for lepton) Thermal masses are neglected. energy/momentum transfer from the bubble wall to leptons xcut = |kout| − |kin| 2T = 1 2
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SLIDE 16 16

Temperature for phase transition

sphaleron decouple leptogenesis via PT sphaleron process
 in equilibrium EW scale Big Bang TeV scale GeV scale 1012 GeV Seesaw scale 
 (1014 GeV) 109 GeV 106 GeV T ∼ 1011 GeV f` ∼ O(102)m2 ⌫ v4 H T 2 T ∼ O(10) p ∆f` v2 H m⌫ ∼ (0.1eV)2 Im{tr[m0 νm∗ ν]} ∼ m2 ν nB ≈ −1 3n` ηB
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SLIDE 17

Thank you very much!

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 coefficient of the Weinberg
  • perator is triggered by a phase transition.
In order to generate enough baryon-antibaryon asymmetry, the temperature for phase transition should be around 1011 GeV.

Summary

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SLIDE 18

Back up

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SLIDE 19

Closed Time Path (CTP) approach

Propagators 19 Dispersion relations Kadanoff-Baym equation t1 t2 Lepton asymmetry Self energy correction Collision term CPV source SH = ST − 1 2(S> + S<) ΣH = ΣT − 1 2(Σ> + Σ<) ∆n`↵(x) = −1 2tr n γ0⇥ S< ↵↵(x, x) + S> ↵↵(x, x) ⇤o ∆f`α(k) = − Z tf ti dt1∂t1tr[γ0S< ~ k (t1, t1) + γ0S> ~ k (t1, t1)] ST αβ(x1, x2) = hT[`α(x1)`β(x2)]i ST αβ(x1, x2) = hT[`α(x1)`β(x2)]i S< αβ(x1, x2) = h`β(x2)`α(x1)i S> αβ(x1, x2) = h`α(x1)`β(x2)i i∂ /S<,> ΣH S<,> Σ<,> SH = 1 2 ⇥ Σ> S< Σ< S>⇤ xµ 1 = (t1, ~ x1) xµ 2 = (t2, ~ x2) Feynman Dyson Wightman
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SLIDE 20

Classical formalism vs CTP formalism

20 CPV source in
 classical formalism Self energies 
 including CPV source 
 in CTP formalism + × + Leptogenesis via RH neutrino decay Leptogenesis via RH neutrino oscillation × Im Im CPV source in
 classical formalism Self energy including CPV source in CTP formalism Anisimov, Buchmuller, Drewes, Mendizabal, 1012.5821
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SLIDE 21

Influence of phase transition

21 Multi-scalar phase transition (in the thick-wall limit) e.g., Silvia Pascoli, Jessica Turner, YLZ, in progress time-dependent integration space-dependent integration ∆nII ` ∝ Im{tr[λ∗(x)∂zλ(x)]} Z d4r r3 M ∆nI ` ∝ Im{tr[λ∗(x)∂tλ(x)]} Z d4r r0 M Interferences of different scalar VEVs cannot be neglected. Time derivative/spatial gradient λ(x) = λ0 + λ1f1(x) + λ2f2(x) Im{tr[λ∗(x1)λ(x2)]} = Im{tr[λ0λ1∗]}[f1(x1) − f1(x2)] + Im{tr[λ0λ2∗]}[f2(x1) − f2(x2)] +Im{tr[λ1∗λ2]}[f1(x1)f2(x2) − f1(x2)f2(x1)]
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SLIDE 22

Influence of thermal effects

22 Resummed propagators of the Higgs and leptons thermal equilibrium thermal mass )]} Z d4r r3 M )]} Z d4r r0 M thermal width γH = ImΠ 2mth,H m2 th,H = ReΠ mth,` = ReΣ γ` = ImΣ2 2mth,` By assuming thermal equilibrium in the rest frame of plasma, 
 the space-dependent integration is zero. )]} Z d4r r3 M= 0 Thermal effects influence the time- and space-dependent integration. is invariant under parity transformation M

⇒