Foreword ...................................................... XIX
Preface ....................................................... XXI
1 Historical Introduction .................................... 1
2 The Standard Model ......................................... 9
2.1 Introduction ............................................... 9
2.2 Standard Electroweak Model ................................. 9
2.2.1 Electroweak Gauge Bosons ........................... 10
2.2.2 Standard Model Matter Fields ....................... 10
2.3 Spontaneous Symmetry-Breaking: Mass Generation ............ 13
2.4 Quantization in the Standard Model ........................ 17
2.5 Renormalization in the Standard Model ..................... 19
2.6 Anomalies ................................................. 21
2.6.1 The Axial Anomaly .................................. 21
2.6.2 Gauge Anomalies .................................... 23
2.7 Quantum Chromodynamics .................................... 24
2.8 Higgs Boson and Unitarity in the Standard Model ........... 25
2.9 Theory Considerations on the Higgs Boson Mass ............. 27
2.10 Experimental Tests of the Standard Model .................. 30
2.11 Open Issues in the Standard Model ......................... 32
2.11.1 The Hierarchy Problem .............................. 34
2.11.2 Coupling Constant Unification ...................... 36
2.12 Summary ................................................... 38
2.13 Problems for Chapter 2 .................................... 39
3 Neutrino Masses and Mixing ................................ 41
3.1 Two-Component Formalism ................................... 41
3.2 Quantization of Majorana and Dirac Fermions ............... 43
3.3 The Lepton Mixing Matrix .................................. 45
3.3.1 Lepton Mixing Matrix for Dirac Neutrinos ........... 45
3.3.2 Lepton Mixing Matrix for Majorana Neutrinos:
Unitary Approximation ................................... 47
3.3.3 General Seesaw-Type Lepton Mixing Matrix ........... 48
3.3.3.1 Symmetrical Parametrization of the General
Lepton Mixing Matrix ............................... 48
3.4 The Neutrino Neutral Current in Seesaw-Type Schemes ....... 50
3.5 CP Properties of Majorana Fermions ........................ 50
3.5.1 CP Properties and Neutrinoless Double-Beta Decay ... 51
3.5.2 Electromagnetic Properties of Majorana Neutrinos ... 52
3.5.3 Majorana-Dirac 'Confusion Theorem' ................. 53
3.6 Summary ................................................... 54
3.7 Problems for Chapter 3 .................................... 54
4 Neutrino Oscillations ..................................... 57
4.1 Preliminaries ............................................. 57
4.2 Neutrino Oscillations Formalism In Vacuo .................. 57
4.3 Matter Effects in Neutrino Oscillations ................... 62
4.4 Neutrino Oscillation Data ................................. 65
4.4.1 Solar Neutrino Data ................................ 65
4.4.2 Reactor Neutrino Data .............................. 67
4.4.3 Atmospheric Neutrino Data .......................... 69
4.4.4 Accelerator Neutrino Data .......................... 73
4.4.5 The Measurement of θ13 ............................. 74
4.5 Global Neutrino Oscillation Analysis ...................... 76
4.6 Global Fit Results for Neutrino Oscillation Parameters .... 77
4.7 Summary and Outlook ....................................... 80
4.8 Problems for Chapter 4 .................................... 83
5 Robustness of Oscillations: The Case of Solar Neutrinos ... 87
5.1 Theoretical Preliminaries: Beyond the Standard Model ...... 88
5.2 Beyond the Standard Solar Model ........................... 91
5.3 Oscillations with Spin-Flavour Precession ................. 94
5.4 Constraining Neutrino Magnetic Moments .................... 97
5.5 Summary .................................................. 100
5.6 Problems for Chapter 5 ................................... 100
6 Absolute Neutrino Masses ................................. 103
6.1 Preliminaries ............................................ 103
6.2 Beta-Decay and Direct Searches for Neutrino Mass ......... 103
6.2.1 Relativistic Beta-Decay Kinematics ................ 104
6.2.2 Beta Decay in the Three-Neutrino Case ............. 106
6.3 Neutrinoless Double-Beta Decay ........................... 110
6.4 Light-Neutrino Exchange 0νββ Mechanism ................... 112
6.5 Experimental Prospects in the Search for 0νββ ............ 115
6.6 Neutrinoless Double-Beta Decay in Flavour Models ......... 115
6.7 Short-Range Contributions to 0νββ Decay and the Weak
Interaction Scale ........................................ 117
6.8 Black Box and the Significance of Oνßß ................... 120
6.9 Summary .................................................. 121
6.10 Problems for Chapter 6 ................................... 121
7 Neutrino Masses in SU(3)C SU(2)LU(1)γ Theories .......... 123
7.1 Preliminaries: The Origin of Neutrino Mass ............... 123
7.2 Effective Seesaw Mechanism: Explicit Lepton Number
Violation ................................................ 125
7.3 Seesaw Dynamics in SU(3)CSU(2)LU(1)γ and the
Majoron .................................................. 127
7.3.1 Basic Considerations .............................. 127
7.3.2 The Majoron in the SU(3)CSU(2)LU(1)γ Seesaw ..... 128
7.3.3 The Structure of Majoron Couplings: Type I
Seesaw Example .................................... 130
7.3.4 Inverse SU(3)CSU(2)LU(1)γ Seesaw Mechanism ...... 132
7.4 Summary .................................................. 134
7.5 Problems for Chapter 7 ................................... 134
8 Higgs Boson Physics and Neutrinos ........................ 135
8.1 Higgs Production in the Standard Model ................... 135
8.1.1 Higgs Production at Electron-Positron Colliders ... 136
8.1.1.1 Higgs-Strahlung Processes ..................... 136
8.1.1.2 Vector Boson Fusion ........................... 136
8.1.2 Higgs Production at Hadron Colliders .............. 139
8.1.2.1 Associated Production with the W/Z Bosons ..... 140
8.1.2.2 The Vector Boson Fusion Mechanism ............. 141
8.1.2.3 The Gluon-Gluon Fusion Process ................ 141
8.1.2.4 Associated Production with Heavy Quarks ....... 142
8.2 Higgs Decays in the Standard Model ....................... 142
8.2.1 Decays into Fermions: Quarks and Leptons .......... 143
8.2.2 Decays into W/Z Gauge Bosons ...................... 143
8.2.2.1 Two-Body Final States ......................... 144
8.2.2.2 Three-Body Final States ....................... 144
8.2.2.3 Four-Body Final States ........................ 145
8.2.3 Loop-Induced Higgs Boson Decays: γγ, γZ and gg .... 145
8.2.3.1 H → γγ ....................................... 145
8.2.3.2 H → Zγ ........................................ 146
8.2.3.3 H → gg ........................................ 147
8.2.3.4 Standard Model Higgs Boson Branching Ratio
Summary ....................................... 147
8.3 Higgs Physics in Models with Low-Scale Lepton Number
Violation ................................................ 147
8.3.1 Invisible Higgs Boson Decays ...................... 148
8.4 Summary .................................................. 750
8.5 Problems for Chapter 8 ................................... 757
9 Supersymmetry ............................................ 753
9.1 Introduction and Motivation .............................. 753
9.2 Supersymmetry Algebra and Representations ................ 755
9.1 Supersymmetry Algebra .................................... 155
9.2.2 Implications of the Supersymmetry Algebra ......... 156
9.2.3 Supersymmetry Representations ..................... 157
9.2.3.1 Massive Case .................................. 157
9.2.3.2 Massless Case ................................. 158
9.3 How to Build a Supersymmetric Model ...................... 158
9.3.1 Kinetic Terms ..................................... 159
9.3.2 Interactions ...................................... 159
9.3.2.1 Self-Interactions of the Gauge Multiplet ...... 159
9.3.2.2 Interactions of the Gauge and Matter
Multiplets .................................... 159
9.3.2.3 Self- Interactions of the Matter Multiplet .... 160
9.3.3 Supersymmetry-Breaking Lagrangian ................. 160
9.3.4 R-Parity .......................................... 161
9.4 The Minimal Supersymmetric Standard Model ................ 162
9.4.1 The Gauge Group and Particle Content .............. 162
9.4.2 The Superpotential and Supersymmetry-Breaking
Lagrangian ........................................ 164
9.4.3 Spontaneous Symmetry-Breaking ..................... 164
9.4.4 MSSM Scalar Potential: UFB Directions and CCB
Mminima ........................................... 165
9.4.5 The Constrained Minimal Supersymmetric Standard
Model ............................................. 167
9.5 Mass Matrices in the MSSM ................................ 168
9.5.1 Gaugino Mass Matrices ............................. 168
9.5.1.1 The Chargino Mass Matrix ...................... 168
9.5.1.2 The Neutralino Mass Matrix .................... 169
9.5.2 Higgs Boson Mass Matrices ......................... 170
9.5.2.1 Neutral Higgs Mass Matrix ..................... 170
9.5.2.2 Charged Higgs Mass Matrix ..................... 172
9.5.3 Fermion Mass Matrices ............................. 172
9.5.3.1 Charged Lepton Mass Matrix .................... 172
9.5.3.2 Quark Mass Matrices ........................... 173
9.5.4 Sfermion Mass Matrices ............................ 174
9.5.4.1 Slepton Mass Matrices ......................... 174
9.5.4.2 Sneutrino Mass Matrices ....................... 175
9.5.4.3 Squark Mass Matrices .......................... 175
9.6 Couplings in the MSSM .................................... 176
9.6.1 Charged Current Couplings as an Example ........... 176
9.6.2 Other Couplings ................................... 179
9.7 Coupling Constant Unification ............................ 179
9.8 Experimental Constraints on the MSSM ..................... 180
9.9 Summary .................................................. 180
9.10 Problems for Chapter 9 .............................. 182
10 Spontaneous R-Parity Violation ........................... 183
10.1 Introduction ............................................. 183
10.2 A Viable Spontaneous R-Parity-Breaking Model ............. 184
10.3 Symmetry-Breaking ........................................ 186
10.3.1 Tree-Level Breaking ............................... 187
10.3.2 Radiative Symmetry-Breaking ....................... 188
10.4 Main Features of the Model ............................... 189
10.4.1 Chargino Mass Matrix .............................. 190
10.4.2 Neutralino Mass Matrix ............................ 190
10.4.3 Charged-Current Couplings ......................... 191
10.4.4 Neutral Current Couplings ......................... 191
10.5 Implications for the Electroweak Breaking Sector ......... 192
10.5.1 Higgs Spectrum .................................... 192
10.5.2 Higgs Boson Production ............................ 193
10.5.3 CP-Even Higgs Boson Decays ........................ 195
10.5.4 CP-Odd Higgs Boson Decays ......................... 196
10.6 Summary .................................................. 197
10.7 Problems for Chapter 10 .................................. 198
11 Bilinear R-Parity Violation .............................. 199
11.1 The Model ................................................ 199
11.2 The Scalar Potential ..................................... 200
11.3 Mass Matrices in the BRpV Model .......................... 201
11.3.1 Chargino Mass Matrix .............................. 202
11.3.2 Neutralino Mass Matrix ............................ 203
11.4 Couplings in the BRpV Model .............................. 203
11.4.1 Charged Current Couplings ......................... 204
11.5 Neutrino Masses and Mixings in the BRpV Model ............ 205
11.5.1 Tree-Level Structure .............................. 205
11.5.2 One-Loop Neutrino Masses and Mixings .............. 206
11.5.2.1 Definition .................................... 206
11.5.2.2 Relevant Diagrams ............................. 206
11.5.2.3 Gauge Invariance .............................. 207
11.5.3 The One-Loop Mass Matrix .......................... 208
11.6 Neutrino Properties and BRpV Parameters .................. 208
11.6.1 The Atmospheric Neutrino Sector ................... 208
11.6.2 The Solar Neutrino Sector ......................... 210
11.6.3 Constraining the BRpV Parameters .................. 211
11.7 Approximate Formulae for the Neutrino Masses and
Mixings .................................................. 211
11.7.1 Approximate Rotation Matrices ..................... 212
11.7.2 Approximate Coupling Expressions .................. 274
11.7.3 Relevant Topologies ............................... 214
11.7.4 The Solar Mass Scale .............................. 216
11.7.5 The Solar Mixing Angle ............................ 217
11.8 Summary .................................................. 219
11.9 Problems for Chapter 11 ............................. 219
12 Phenomenology of Bilinear R-Parity Violation ............. 221
12.1 LSP Production ........................................... 221
12.2 LSP Decays ............................................... 223
12.2.1 LSP Decay Length and Displaced Vertices ........... 223
12.2.2 LSP Decay Modes ................................... 223
12.3 Probing Neutrino Mixing via Neutralino Decays ............ 226
12.4 Other LSP Scenarios ...................................... 230
12.4.1 Stau as Lightest Supersymmetric Particle .......... 230
12.4.2 Stop as Lightest Supersymmetric Particle .......... 233
12.5 Summary .................................................. 234
12.6 Problems for Chapter 12 .................................. 234
13 Neutrino Masses and Left-Right Symmetry .................. 237
13.1 Preliminaries: SU(3)CSU(2)LSU(2)RU(l) Symmetry ..... 237
13.2 'Standard' SU(3)CSU(2)LSU(2)RU(l) Symmetric
Seesaw ................................................... 239
13.3 Low-Scale SU(3)CSU(2)LSU(2)RU(l) Seesaw Mechanisms ... 241
13.4 Experimental Constraints ................................. 242
13.5 Direct Searches for the Messengers of Neutrino Mass ...... 243
13.6 Summary .................................................. 246
13.7 Problems for Chapter 13 .................................. 247
14 Neutrino Masses and Unification .......................... 249
14.1 Preliminaries: Unification in SU(5) ...................... 249
14.2 Neutrinos in SU(5) ....................................... 252
14.3 Neutrinos in SO(10) ...................................... 254
14.4 Low-Scales in SO(10) Models: Intermediate Gauge
Symmetries ............................................... 256
14.4.1 Model Class-I: One Intermediate Left-Right Scale .. 257
14.4.2 Model Class-II: Additional Intermediate Pati-
Salam Scale ....................................... 258
14.4.3 Models with an Intermediate U(1)R × U(1)B-L
Scale ............................................. 259
14.5 Neutrino Seesaw in Low-Scale SO(10) model ................ 259
14.6 Non Supersymmetric Low-Scale Models ...................... 263
14.7 Summary .................................................. 263
14.8 Problems for Chapter 14 .................................. 264
15 Lepton Flavour Violation ................................. 265
15.1 Charged Lepton Flavour Violation ......................... 265
15.1.1 Lepton-Flavour-Violating Muon Decays .............. 265
15.1.2 μ — e Conversion in Nuclei ........................ 268
15.2 Models for Charged Lepton Flavour Violation .............. 269
15.2.1 Low-Scale Seesaw Models ........................... 269
15.2.2 High-Scale Seesaw Models .......................... 271
15.2.2.1 Supersymmetric Type I Seesaw .................. 272
15.2.2.2 Supersymmetric Type II Seesaw ................. 274
15.2.3 Lepton Flavour Violation at the High-Energy
Frontier .......................................... 275
15.2.3.1 Lepton Flavour Violation in Slepton Decays .... 276
15.2.3.2 Slepton Mass Splittings ....................... 278
15.2.3.3 Lepton Flavour Violation in the Decays of
Right-Handed Neutrinos ........................ 279
15.3 Summary and Prospects .................................... 281
15.4 Problems for Chapter 15 .................................. 281
16 The Flavour Problem and the Quest for Family Symmetry .... 283
16.1 Preliminaries ............................................ 283
16.2 Reference Neutrino Mixing Patterns ....................... 285
16.2.1 Tri-Bimaximal Pattern ............................. 285
16.2.2 Bi-Large Neutrino Mixing Pattern .................. 287
16.3 Prototype Flavour Model with Tetrahedral Symmetry ........ 289
16.4 Revamped A4 Flavour Model: Generating θ13 ................ 293
16.4.1 Minimal Flavon Extension with θ13 ≠ 0 ............. 293
16.4.2 Neutrino Oscillation Parameters ................... 294
16.5 Fermion Masses in a Realistic A4-Based Standard Model .... 296
16.5.1 Quark-Lepton Mass Relation in a Realistic A4
Extension of the Standard Model ................... 297
16.5.2 The Charged Lepton-Quark Mass Relation ............ 298
16.5.3 Quark Mixing: The CKM Matrix ...................... 299
16.5.4 Neutrino Masses and Mixing ........................ 300
16.6 Quarks, Non-Abelian Discrete Flavour Symmetries and
Unification .............................................. 302
16.7 Summary and Prospects .................................... 303
16.8 Problems for Chapter 16 .................................. 304
17 Cosmological Implications of Neutrino Masses ............. 307
17.1 The very Beginning: Inflation and Primordial Density
Perturbations ............................................ 307
17.2 The Cosmic Microwave Background .......................... 309
17.3 Neutrino Cosmology for Pedestrians ....................... 310
17.3.1 Neutrino Decoupling ............................... 311
17.3.2 The Cosmic Neutrino Background .................... 313
17.3.3 Primordial Big Bang Nucleosynthesis ............... 314
17.4 Dark Matter in the Universe .............................. 315
17.4.1 Evidence for Dark Matter in the Universe .......... 316
17.4.2 Dark Matter and Large-Scale Structure in the
Universe .......................................... 319
17.5 Dark Matter Detection .................................... 320
17.6 Neutrino Mass Generation and Dark Matter Candidates ...... 323
17.6.1 Massive Neutrinos as Dark Matter? ................. 324
17.6.2 WIMP Dark Matter as Neutrino Mass Messenger ....... 324
17.6.2.1 The Particle Content .......................... 325
17.6.2.2 Yukawa Interactions and Fermion Masses ........ 326
17.6.2.3 Radiative Seesaw Neutrino Masses .............. 328
17.6.2.4 Fermionic Dark Matter in Radiative Seesaw
Scheme ........................................ 328
17.6.3 WIMP Dark Matter Stabilized by Flavour Symmetry ... 332
17.6.4 Supersymmetric WIMP Dark Matter ................... 334
17.6.5 Majoron as Decaying Dark Matter ................... 336
17.6.6 Decaying Gravitino as Dark Matter ................. 338
17.7 Summary .................................................. 339
17.8 Problems for Chapter 17 .................................. 340
A Notation and Conventions ................................. 341
A.l Special Relativity and Dirac Matrices .................... 341
A.2 Two-Component Spinor Notation ............................ 342
A.3 Relating Two-Component and Four-Component Spinors ........ 344
В Feynman Rules for Majorana Fermions ...................... 347
B.l Feynman Rules ............................................ 347
B.l.l External Fermions .................................. 348
B.1.2 Propagators ........................................ 349
B.1.3 Couplings .......................................... 350
B.2 A Simple Example ......................................... 352
С Feynman Rules for the Standard Model ..................... 355
C.l Introduction ............................................. 355
C.2 The Complete Standard Model Lagrangian ................... 355
C.2.1 The Gauge Field Lagrangian ........................ 355
C.2.2 The Fermion Fields Lagrangian ..................... 355
C.2.3 The Higgs Boson Lagrangian ........................ 356
C.2.4 The Yukawa Lagrangian ............................. 356
C.2.5 The Gauge Fixing Term ............................. 356
C.2.6 The Ghost Lagrangian .............................. 357
C.3 The Feynman Rules for QCD ................................ 358
C.3.1 Propagators ....................................... 358
C.3.2 Triple Gauge Interactions ......................... 358
C.3.3 Quartic Gauge Interactions ........................ 358
C.3.4 Fermion Gauge Interactions ........................ 359
C.3.5 Ghost Interactions ................................ 359
C.4 The Feynman Rules for the Electroweak Theory ............. 359
C.4.1 Propagators ....................................... 359
C.4.2 Triple Gauge Interactions ......................... 360
C.4.3 Quartic Gauge Interactions ........................ 360
C.4.4 Charged Current Interaction ....................... 361
C.4.5 Neutral Current Interaction ....................... 361
C.4.6 Fermion-Higgs and Fermion-Goldstone Interactions .. 362
C.4.7 Triple Higgs-Gauge and Goldstone-Gauge
Interactions ...................................... 362
C.4.8 Quartic Higgs-Gauge and Goldstone-Gauge
Interactions ...................................... 364
C.4.9 Triple Higgs and Goldstone Interactions ........... 366
C.4.10 Quartic Higgs and Goldstone Interactions .......... 367
С.4.11 Ghost Propagators ................................. 368
C.4.12 Ghost Gauge Interactions .......................... 368
C.4.13 Ghost Higgs and Ghost Goldstone Interactions ...... 370
D Minimal Supersymmetric Standard Model Couplings .......... 373
D.l Charged Current Couplings ................................ 373
D.2 Neutral Current Couplings ................................ 374
D.3 Scalar Couplings to Fermions ............................. 374
E The Prototype Flavour Group: A4 .......................... 377
F Mass Matrices and Couplings in the BRpV Model ............ 381
F.l Mass Matrices ............................................ 381
F.l.l Charged Scalars ................................... 381
F.1.2 CP-Even Neutral Scalars ........................... 383
F.1.3 CP-Odd Neutral Scalars ............................ 384
F.1.4 Squark Mass Matrices .............................. 385
F.l.5 Chargino and Neutralino Mass Matrices ............. 386
F.1.6 Quark Mass Matrices ............................... 386
F.2 Couplings ................................................ 386
F.2.1 Charged Current Couplings ......................... 386
F.2.2 Neutral Current Couplings ......................... 386
F.2.3 Charged Scalars Couplings to Fermions ............. 387
F.2.4 Neutral Scalars Couplings to Fermions ............. 387
G Feynman Diagrams for Dark Matter Annihilation ............ 391
References ............................................... 393
Acknowledgments for the Figures ............................... 419
Index ......................................................... 421
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