Quasiparticles in Leptogenesis [Elektronische Ressource] : A hard-thermal-loop study / Clemens Kießig. Betreuer: Georg Raffelt

Clemens Kießig

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2011
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Quasiparticles in Leptogenesis
A hard-thermal-loop study
Clemens Paul Kie ig
Munchen 2011Quasiparticles in Leptogenesis
A hard-thermal-loop study
Clemens Paul Kie ig
Dissertation
an der Fakult at fur Physik
der Ludwig{Maximilians{Universit at
Munc hen
vorgelegt von
Clemens Paul Kie ig
aus Starnberg
Munc hen, den 1. April 2011This thesis is based on the author’s work partly published in [1{4] conducted from November
2007 until March 2011 at the Max{Planck{Institut fur Physik (Werner{Heisenberg{Institut),
Munc hen, under the supervision of Dr. Michael Plumac her.
Erstgutachter: PD Dr. Georg Ra elt
Zweitgutachter: Prof. Dr. Gerhard Buchalla
Tag der mundlic hen Prufung: 29. Juni 2011Table of Contents
Abstract viii
Zusammenfassung x
Introduction 1
1 Leptogenesis 5
1.1 The Matter-Antimatter Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Sakharov’s Legacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Why Does the Standard Model Fail? . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 B non-conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 C and CP violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3 Deviation from thermal equilibrium . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.4 Ways out: baryogenesis theories . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 The unbearable lightness of neutrino masses and the seesaw . . . . . . . . . . 10
1.4.2 Sakharov and leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.3 A simple model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Thermal Field Theory 19
2.1 Green’s Functions at Finite Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Imaginary Time Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 The Scalar Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 The Dirac Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Hard Thermal Loop Resummation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.1 HTL self energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.2 E ective propagators and dispersion relations . . . . . . . . . . . . . . . . . . 30
2.5.3 HTL resummation technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 33vi Table of Contents
3 Decays and Inverse Decays 37
3.1 The Quest of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 Discontinuity of the Fermion Self-Energy in Yukawa Theory . . . . . . . . . . . . . . 39
3.3 Decays at High Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Application to Leptogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 CP-Asymmetries 49
4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 The Vertex Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1 Going to nite temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.2 Frequency sums for HTL fermion propagators . . . . . . . . . . . . . . . . . . 54
4.2.3 The frequency sum for the vertex contribution . . . . . . . . . . . . . . . . . 55
4.3 The Self-Energy Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Imaginary Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1 Regarding the N cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592
0 04.4.2 Vertex cut throughf‘;g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.4.3 Self-energy cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Analytic Expressions for the CP -Asymmetries . . . . . . . . . . . . . . . . . . . . . . 61
0 04.5.1 Vertex cut throughf‘;g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5.2 Self-energy cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.3 Symmetry under lepton-mode exchange . . . . . . . . . . . . . . . . . . . . . 63
4.6 The CP -Asymmetry at High Temperature . . . . . . . . . . . . . . . . . . . . . . . . 64
4.7 One-Mode Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.8 Temperature-Dependence of the CP -Asymmetries . . . . . . . . . . . . . . . . . . . . 69
5 Boltzmann Equations 75
5.1 Particle Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 Low Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 Neutrino evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.2 Lepton asymmetry evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3 High temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.1 Neutrino evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.3.2 Lepton asymmetry evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4 Interacting Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.5 One-Mode Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.6 Evaluation of the Boltzmann Equations . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.6.1 Weak washout for zero initial abundance . . . . . . . . . . . . . . . . . . . . . 93
5.6.2 Strong and intermediate washout for zero initial abundance . . . . . . . . . . 96Table of Contents vii
5.6.3 Non-zero initial abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.6.4 Final lepton asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Conclusions 107
A Green’s Functions at Zero Temperature 111
B Analytic Solution of the Dispersion Relations for HTL Fermions 113
C Quantities at Zero Temperature 115
C.1 Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
C.2 CP -Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
C.3 Boltzmann Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
D The Other Cuts 121
D.1 Imaginary Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
0D.1.1 Vertex cut throughfN ;g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1212
0D.1.2 Vertex cutfN ;‘g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1222
D.2 Analytic Expressions for the CP -Asymmetries . . . . . . . . . . . . . . . . . . . . . . 122
0D.2.1 Vertex cut throughfN ;g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1222
0D.2.2 Vertex cutfN ;‘g . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1232
E Subtraction of On-Shell Propagators 125
E.1 Low Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
E.2 High Temp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Bibliography 131
Acknowledgments 140Abstract
We analyse the e ects of thermal quasiparticles in leptogenesis using hard-thermal-loop-resummed
propagators in the imaginary time formalism of thermal eld theory. We perform our analysis in
a leptogenesis toy model with three right-handed heavy neutrinos N , N and N . We consider1 2 3
decays and inverse decays and work in the hierarchical limit where the mass of N is assumed to2
be much larger than the mass ofN , that isM M . We neglect avour e ects and assume that1 2 1
the temperatures are much smaller than M and M . We pay special attention to the in uence of2 3
fermionic quasiparticles. We allow for the leptons to be either decoupled from each other, except
for the interactions with neutrinos, or to be in chemical equilibrium by some strong interaction,
for example via gauge bosons. In two additional cases, we approximate the full hard-thermal-loop
lepton propagators with zero-temperature propagators, where we replace the zero-temperature
mass by the thermal mass of the leptons m (T ) in one case and the asymptotic mass of the‘p
positive-helicity mode 2m (T ) in the other case. We calculate all relevant decay rates and CP -‘
asymmetries and solve the corresponding Boltzmann equations we derived. We compare the nal
lepton asymmetry of the four thermal cases and the vacuum case for three di erent initial neutrino
abundances; zero, thermal and dominant abundance. The nal asymmetries of the thermal cases
di er considerably from the vacuum case and from each other in the weak washout regime for zero
abundance and in the intermediate regime for dominant abundance. In the strong washout regime,
where no in uences from thermal corrections are commonly expected, the nal lepton asymmetry
can be enhanced by a factor of two by hiding part of the lepton asymmetry in the quasi-sterile
minus-mode in the case of strongly interacting lepton modes.