1 Neutrino masses and BSM physics 7

Contents

Remerciements i

Abstract (English/Français/Deutsch) iii

Introduction 1

1 Neutrino masses and BSM physics 7

1.1 Neutrino oscillations . . . . 8

1.1.1 Puzzles from neutrino fluxes . . . . 8

1.1.2 Theory of neutrino oscillations . . . . 8

1.1.3 Experimental framework . . . 10

1.2 Non-oscillation experiments . . . 12

1.2.1 Ø-decay . . . 12

1.2.2 Neutrinoless double Ø-decay (0∫2Ø) . . . 13

1.2.3 Cosmology . . . 13

1.3 Neutrino mass, effective Lagrangian and Seesaw mechanisms . . . 14

1.3.1 Effective Lagrangian and new physics . . . 15

1.3.2 Type-1 Seesaw mechanism . . . 17

1.3.3 Type-2 Seesaw mechanism . . . 19

1.3.4 Type-3 Seesaw mechanism . . . 22

1.4 Dimension-6 operators and CLFV processes . . . 22

1.5 Inverse Seesaw models . . . 24

1.6 SO(10) GUT and L-R symmetry motivations for Seesaw models . . . 26

1.6.1 SO(10) GUT group . . . 26

1.6.2 L-R symmetric model . . . 27

2 Muon to electron conversion in nuclei in type-1 Seesaw models 31 2.1 Type-1 Lagrangian in the mass eigenstate basis . . . 31

2.2 Charged Lepton Flavor Violation processes . . . 34

2.2.1 Experimental status . . . 35

2.2.2 Theoretical status in the Seesaw models . . . 38

2.3 µ ! e conversion rate for type-1 Seesaw models . . . 39

2.3.1 General expression of the conversion rate and approximations . . . 40

2.3.2 Methodology . . . 47

2.3.3 Computation of the rate in type-1 Seesaw models . . . 48

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2.4 Predictions and constraints : degenerate case . . . 53

2.4.1 Ratios of rates involving one same flavour transition . . . 54

2.4.2 Large mass regime (m

∏ m

) and constraints on the mixing parameters . . 57

2.4.3 Low mass regime (m

∑ m

) and constraints on the mixing parameters . . . 59

2.4.4 Comments . . . 63

2.5 Ratios of rates involving one same flavor transition : non degenerate case . . . 64

2.5.1 Casas-Ibarra parametrization . . . 64

2.5.2 n

= 2 non-degenerate right-handed neutrinos . . . 65

2.5.3 n

= 3 non-degenerate right-handed neutrinos . . . 69

2.6 Comparison between the different types of Seesaw . . . 69

2.6.1 Type-2 Seesaw ratios and maximum scales . . . 70

2.6.2 Type-3 Seesaw ratios and maximum scale . . . 71

2.6.3 Distinction between the Seesaw . . . 73

2.7 Summary . . . 75

3 The Baryon Asymmetry of the Universe and standard leptogenesis 79 3.1 Experimental determination of the baryon density . . . 81

3.1.1 From the Cosmic Microwave Background (CMB) . . . 82

3.1.2 From Big Bang Nucleosynthesis (BBN) . . . 82

3.2 Needed ingredients for baryogenesis . . . 83

3.3 Baryogenesis possibilities . . . 85

3.3.1 Electroweak baryogenesis . . . 85

3.3.2 GUT Baryogenesis . . . 86

3.3.3 Sphalerons and baryogenesis through leptogenesis . . . 86

3.4 Basics of Leptogenesis : the unflavored type-1 Seesaw case . . . 88

3.4.1 Lagrangian and interactions . . . 88

3.4.2 Unflavored statement and general scenario . . . 89

3.4.3 Tree-level decay rate . . . 90

3.4.4 Evaluation of the C P -asymmetry . . . 91

3.4.5 Boltzmann equations . . . 93

3.4.6 Analytical solutions to the Boltzmann equations . . . 97

3.4.7 Some results of successful leptogenesis . . . 99

3.5 Flavor issue in type-1 leptogenesis . . . 101

3.6 Flavored type-1 leptogenesis . . . 104

3.6.1 Tree-level decay rates . . . 104

3.6.2 Evaluation of the C P -asymmetry . . . 105

3.6.3 Boltzmann equations . . . 105

3.6.4 Analytical solutions to the Boltzmann equations . . . 106

3.6.5 Some results of successful leptogenesis . . . 107

3.7 Additional scattering processes . . . 109

4 Type-2 Seesaw leptogenesis 111 4.1 One-flavor approximation of the type-2 leptogenesis . . . 113

4.1.1 Lagrangians and interactions . . . 113

4.1.2 One-flavor approximation statement . . . 114

4.1.3 Tree-level decay rates . . . 114

4.1.4 Evaluation of the C P-asymmetry . . . 116

4.1.5 Boltzmann equations . . . 117

4.1.6 Analytical resolution of the Boltzmann equations and maximum B ° L asym- metry reachable . . . 122

4.1.7 Some results of successful leptogenesis . . . 127

4.2 Flavor issue in type-2 leptogenesis . . . 130

4.2.1 Flavor regimes . . . 131

4.2.2 Parameter space of the flavor regimes . . . 133

4.3 Flavored type-2 leptogenesis . . . 136

4.3.1 Tree-level decay rates . . . 137

4.3.2 Computation of the C P -asymmetries . . . 138

4.3.3 B/3 ° L

asymmetries and chemical equilibrium conditions . . . 141

4.3.4 Flavored Boltzmann equations . . . 145

4.3.5 Formal integration of Boltzmann equations . . . 146

4.4 Summary : leptogenesis procedure to follow in any given type-2 Seesaw model . . . 150

4.5 Purely Flavored Leptogenesis . . . 151

4.5.1 Mechanism . . . 152

4.5.2 PFL scenario efficiency . . . 155

4.5.3 Minimal and maximal B ° L asymmetry . . . 161

4.6 General triplet flavored leptogenesis . . . 164

4.6.1 Efficiency-like parameter . . . 164

4.6.2 Successful leptogenesis . . . 168

4.7 Compatibility with CLFV processes . . . 168

4.8 Summary . . . 169

5 Asymmetric dark matter in the Inert Doublet Model 173 5.1 Generalities . . . 174

5.1.1 Evidences for dark matter . . . 174

5.1.2 DM properties . . . 174

5.2 Models for dark matter . . . 175

5.2.1 Scalar singlet. . . . 175

5.2.2 The Inert Doublet Model (IDM) . . . 177

5.2.3 Other possibilities . . . 178

5.3 Dark matter detection and constraints . . . 179

5.3.1 Direct Detection . . . 180

5.3.2 Indirect Detection . . . 181

5.3.3 Collider constraints . . . 183

5.4 Dark matter production mechanisms . . . 184

5.4.1 Symmetric production and WIMP miracle . . . 184

5.4.2 Asymmetric production . . . 188

5.5 Inert Scalar Doublet Asymmetry as the origin of dark matter . . . 189

5.5.1 Asymmetric production and depletion of the H

density . . . 191

5.5.2 Final inert scalar relic density . . . 200

5.5.3 Failure of the asymmetric IDM scenario . . . 201

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5.5.4 Reprocessing the inert doublet asymmetry into a lighter particle DM relic

density . . . 204

5.6 Summary . . . 207

General conclusion 209 A Units and conversion factors 213 A.1 Natural units . . . 213

A.2 Parameters and constants . . . 213

B µ to e conversion in atomic nuclei 215 B.1 Some useful identities . . . 215

B.2 Feynman rules . . . 215

B.3 Feynman diagrams and associated amplitudes . . . 217

B.3.1 Methodology . . . 217

B.3.2 Photon Penguin contribution . . . 218

B.3.3 Z Penguin contribution . . . 222

B.3.4 W boxes contribution . . . 225

B.4 Summary . . . 228

B.5 Integrals . . . 232

C Tools for leptogenesis and dark matter genesis 235 C.1 Thermodynamics of the early Universe : definitions and conventions . . . 235

C.1.1 Bosons . . . 235

C.1.2 Fermions . . . 236

C.1.3 Maxwell-Boltzmann . . . 237

C.1.4 Gas properties in the early Universe . . . 237

C.1.5 Equilibrium . . . 239

C.2 Sphalerons . . . 239

C.3 Boltzmann equations or chemical equilibrium conditions ? . . . 240

C.4 Boltzmann equations formalism . . . 241

C.4.1 Generalities . . . 241

C.4.2 Method . . . 242

C.4.3 Example : the type-1 leptogenesis . . . 243

C.5 Chemical equilibrium conditions . . . 244

C.5.1 Generalities and usual chemical equilibrium conditions . . . 244

C.5.2 Temperature regimes and chemical equilibrium conditions for type-1 Seesaw leptogenesis . . . 246

C.5.3 Relation between the baryon, lepton and B ° L asymmetries . . . 249

D Type-2 Seesaw leptogenesis 251 D.1 Tree-level decay rates . . . 251

D.1.1 Leptonic channel . . . 251

D.1.2 Scalar channel . . . 252

D.1.3 Total decay width . . . 253

D.2 C P -asymmetries . . . 253

D.2.1 Pure scalar triplet case . . . 253

D.2.2 Mixed type-1+2 scheme . . . 255

D.3 Scattering rates . . . 256

D.4 Boltzmann equations . . . 257

D.5 Chemical equilibrium conditions . . . 259

E Asymmetric Dark matter in IDM 265 E.1 Scattering rates . . . 265

E.2 Analytical resolution of the Boltzmann equations . . . 266

E.3 Landau Pole . . . 267

Bibliography 269

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