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JoséW. F. Valle and Jorge C. Romão

Neutrinos in High Energy and

Astroparticle Physics

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JoséW. F. Valle and Jorge C. Romão

Neutrinos in High Energy and Astroparticle

Physics

The Authors

Prof. José W. F. Valle

Universitat de València

Inst. de Fısica Corpuscular

Valencia, Spain

Prof. Jorge C. Romao

Instituto Superior Técnico

Centro de Fısica Teórica de Partıculas

Lisboa, Portugal

Cover

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As armas e os Barões assinalados

Que da Ocidental praia Lusitana

Por mares nunca de antes navegados

Passaram ainda além da Taprobana,

Em perigos e guerras esforçados

Mais do que prometia a força humana,

E entre gente remota edificaram

Novo Reino, que tanto sublimaram

Os Lusıadas, Canto I, Luıs de Camões

Minha terra tem palmeiras,

Onde canta o Sabiá;

As aves, que aqui gorjeiam,

Não gorjeiam como lá.

Canção do Exılio, (Gonçalves Dias)

À Guida e Isabel por sua paciência e apoio nessa aventura

À saudosa memoria de meus inesquecíveis pais, Francisca e Raimundo

(J. V.).

IX

Contents

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 andMixing 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

X Contents

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 ‘ConfusionTheorem’ 53

3.6 Summary 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


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


6 Absolute Neutrino Masses 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 theThree-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

Contents XI

6.8 Black Box and the Significance of 0𝜈𝛽𝛽 120

6.9 Summary 121


7 Neutrino Masses in SU(3)c⊗SU(2)L⊗U(1)Y 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)c⊗SU(2)L⊗U(1)Y and the Majoron 127

7.3.1 Basic Considerations 127

7.3.2 The Majoron in the SU(3)c⊗SU(2)L⊗U(1)Y Seesaw 128

7.3.3 The Structure of Majoron Couplings: Type I Seesaw Example 130

7.3.4 Inverse SU(3)c⊗SU(2)L⊗U(1)Y Seesaw Mechanism 132

7.4 Summary 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 150


9 Supersymmetry 153

9.1 Introduction and Motivation 153

9.2 Supersymmetry Algebra and Representations 155

XII Contents

9.2.1 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


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

Contents XIII

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


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 214

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


XIV Contents

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


13 Neutrino Masses and Left–Right Symmetry 237

13.1 Preliminaries: SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1) Symmetry 237

13.2 ‘Standard’ SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1) Symmetric Seesaw 239

13.3 Low-Scale SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1) Seesaw Mechanisms 241

13.4 Experimental Constraints 242

13.5 Direct Searches for the Messengers of Neutrino Mass 243

13.6 Summary 246


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


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

Contents XV

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


16 The Flavour Problem and the Quest for Family Symmetry 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 CKMMatrix 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


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

XVI Contents

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


A Notation and Conventions 341

A.1 Special Relativity and Dirac Matrices 341

A.2 Two-Component Spinor Notation 342

A.3 Relating Two-Component and Four-Component Spinors 344

B Feynman Rules for Majorana Fermions 347

B.1 Feynman Rules 347

B.1.1 External Fermions 348

B.1.2 Propagators 349

B.1.3 Couplings 350

B.2 A Simple Example 352

C Feynman Rules for the Standard Model 355

C.1 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 ElectroweakTheory 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

Contents XVII

C.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.1 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 BRpVModel 381

F.1 Mass Matrices 381

F.1.1 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.1.5 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

XIX

Foreword

Neutrinos are the most fascinating elementary particles and an exciting field of

research. Due to the weakness of their interaction with other particles, they are

called ‘Elusive, Mysterious or Ghost’ particles. Neutrino properties have been

gradually unveiled through the discoveries of a neutrino burst from supernova

SN1987A and of oscillations of atmospheric, solar, reactor and accelerator-

produced neutrinos.This has made them a bit less mysterious. Neutrinos provide

a unique tool to probe deep inside astronomical objects: for instance, the Earth,

the Sun, stars, galactic nuclei, the Big Bang and so on. As the ultimate cosmic

messenger, neutrinos provide information on productionmechanisms happening

in the very early Universe. It is not too much to say that further experimental

and theoretical studies of neutrinos will be decisive in elucidating the nature of

matter and the quest for the origin of the Universe.

The publication of this book is quite timely in summarizing established neutrino

physics as well as exploring the new paradigms. The book presents a comprehen-

sive account of recent developments described for anyone from elementary grad-

uate student level as a textbook to researchers as a handbook. Readers will enjoy a

realistic presentation in which new theoretical ideas sprout new experiments, and

new experimental results trigger new theoretical considerations. Such interplay

between theory and experiment reaps rich harvests in neutrino and astroparticle

physics.

Atsuto Suzuki is the Director General, KEK, of the High Energy Accelerator

Research Organization in Tsukuba and Tokai, Japan.

XXI

Preface

The detection of the Higgs boson and the discovery of neutrino oscillations mark

a turning point in particle physics, whose profound implications are not yet

fully grasped. In particular, underpinning the nature of neutrinos as well as the

origin of their mass and understanding the observed flavour pattern pose a great

challenge in particle physics. This book provides the theoretical basis to describe

recent results in neutrino physics, now brought to the era of precision after the

determination of the third lepton mixing parameter. We start with a brief review

of the standard model, its successes and shortcomings. Then we move on to

a general description of massive neutrinos, stressing the significance of lepton

number violation processes such as neutrinoless double-beta decay in probing

their Majorana nature and the associated charge parity (CP) phases. We give the

necessary theoretical background to describe modern neutrino physics, omitting

the discussion of standard model neutrino cross sections because these can be

found in textbooks such as the ones by Boehm and Vogel (1992) [1], Fukugita

and Yanagida (2003) [2] and Giunti and Kim (2007) [3]. Instead, we focus on the

‘architecture’ of massive neutrino theories, with a thorough discussion of the

seesaw mechanism, its many realizations and the corresponding structure of the

lepton mixing matrix which is a key ingredient to discuss oscillations. These are

treated in detail along with the latest oscillation parameter fits. We also discuss

the non-standard nature of the charged and neutral current weak interactions

and how it could give clues on the neutrino mass generation scale. In discussing

neutrino masses, we adopt a model-builder’s perspective, covering both high-

as well as low-scale physics approaches. Among the latter is the possibility that

the origin of neutrino mass is intrinsically supersymmetric, which makes it

possible to probe neutrino properties also at the high energies available at the

large hadron collider (LHC). The low-scale origin of neutrino mass could also

lead to other implications at accelerators, such as invisible decays of the Higgs

boson.

We also discuss extended gauge models and grand unification, followed by

lepton flavour violation and theories of flavour, emphasizing how neutrinos may

bring fresh insight into unification and the flavour problem.

XXII Preface

We end with a brief discussion of the implications of neutrinos in the early

Universe, from the cosmic microwave background (CMB) and Big Bang nucle-

osynthesis (BBN)1) all the way back to the origin of dark matter.

This textbook should be adequate for graduate students with an introduction to

particle physics and some basic knowledge on quantum field theory such as can

be obtained from selected chapters of Peskin and Schroeder (1995) [5] or Mandl

and Shaw (2010) [6]. Our presentation is mostly explicit throughout the book,

except in parts of the last two chapters, where the view is somewhat panoramic,

though with many references to dedicated textbooks as well as original articles, as

appropriate.

This book is the result of the authors’ friendship and steady collaboration

over 25 years. It has also benefitted from enlightening discussions and/or col-

laborations with many of our colleagues, to whom we are very much indebted.

The long list includes Evgeni Akhmedov, Ignatios Antoniadis, Alfredo Aranda,

Kaladi Babu, John Bahcall (deceased), Juan Barranco, Alfred Bartl, Federica

Bazzocchi, Luis Bento, Zurab Berezhiani, Venya Berezinsky, José Bernabéu,

Gustavo Branco, Cliff Burgess, David Cerdeño, Piotr Chankowski, Fernando de

Campos, Pedro de Holanda, André De Gouvêa, Frank Deppish, Marco Diaz,

Michael Dittmar, Alexander Dolgov, Oscar Eboli, John Ellis, Andreu Esteban,

Amand Faessler, Nicolao Fornengo, Graciela Gelmini, Carlo Giunti, Concha

Gonzalez-Garcia, Walter Grimus, Martin Hirsch, Patrick Huber, Ara Ioannisyan,

Cecilia Jarlskog, Filipe Joaquim, Anjan Joshipura, Stephen King, Paul Langacker,

Luis Lavoura, Manfred Lindner, Roberto Lineros, Mauricio Magro, Antonio

Masiero, Omar Miranda, Rabindra Mohapatra, Stefano Morisi, Celio Moura,

Enrico Nardi, Hiroshi Nunokawa, Heinrich Paes, Stephen Parke, Sergio Pastor,

Eduardo Peinado, Juha Peltoniemi, Orlando Peres, Stefan Pokorski, Werner

Porod, Timur Rashba, Diego Restrepo, Alexander Rez, Signe Riemer-Sørensen,

Nuria Rius, Graham Ross, Anna Rossi, Victor Semikoz, Joe Schechter, David

Schramm (deceased), Arcadi Santamaria, Thomas Schwetz, Dmitry Sokoloff,

Alexei Smirnov, Marco Taoso, Ana Teixeira, Ricard Tomàs, Mariam Tórtola,

Avelino Vicente, Jordi Vidal, Lincoln Wolfenstein, Kai Zuber and many others.

Several topics arose from their work and enthusiasm, and the exchange of insights

and knowledge. We warmly thankMassi Lattanzi for sharing his valuable insights

on cosmology, and Sofiane Boucenna and Lucho Dorame for proofreading.

The cover background picture (courtesy of Stefan Gottlöber) is part of a

collaboration between the MultiDark Project led by Carlos Muñoz and the

Leibniz-Institut für Astrophysik, Potsdam. It shows the dark matter density in a

slice through the MultiDark simulation at redshift z = 0.5. More information and

credits at www.multidark.org. We also thank Wiley-VCH staff for their invitation

and technical assistance.

This work was supported by MINECO FPA2011-22975 and CSD2009-00064.

1) For extensive descriptions of neutrino cosmology, see Gravitation and Cosmology: Principles and

Applications of the General Theory of Relativity by S. Weinerg (1972); The Early Universe by Kolb,

E.W. and Turner, M.S. (1990) and Neutrino Cosmology by Lesgourgues et al. (2013) [4].

http://www.multidark.org.We

1

1

Historical Introduction

The most incomprehensible thing about the universe is that it is comprehen-

sible.

(Albert Einstein)

Physics at the shortest scales deals with the study of the elementary constituents of

matter as produced in particle accelerators or within astrophysical and cosmolog-

ical environments. In broad terms, particle physics seeks to determine the prop-

erties of the Universe at large, starting from themicrophysics describing the inter-

actions among quarks and leptons, the basic building blocks of matter.The under-

lying theory is the so-called standard model (SM), which puts together quantum

mechanics and Einstein’s relativity along with the principle of gauge invariance.

These basic pillars constitute the three revolutions in physics that took place in the

past century.The SM describes the electromagnetic, weak and strong interactions

among the elementary constituents of matter in terms of a quantum field theory

merging quantum mechanics with special relativity and incorporating interac-

tions via gauge symmetry. In this picture, all basic forces other than gravity are

mediated by the exchange of intermediate vector bosons associated with the SM

gauge symmetry group SU(3)c ⊗ SU(2)L ⊗ U(1)Y, that is, the photon, the gluonsand theweak gauge bosonsW± andZ [7–9]. Its theoretical formulationwas devel-

oped from the mid- to the late twentieth century, and its current form has gained

general acceptance after the experimental confirmation of the existence of quarks

in the mid-1970s. Quarks carry colour and hence couple to gluons, while leptons

do not. Today we know for certain that there are three types or ‘generations’ of

elementary constituents of matter.

The gauge bosons associated with the electroweak SU(2)L ⊗ U(1)Y part of the

symmetry are the photon and W±, Z gauge bosons. The latter were directly

produced for the first time at CERN (the European Organization for Nuclear

Research) in 1983 [10–13]. On the other hand, the gluons are associated with

the SU(3) colour symmetry and were discovered at DESY (German Electron

Synchrotron) [14].

In order to provide masses for the gauge bosons and fermions, the SM gauge

symmetry must be broken spontaneously down to the SU(3)c ⊗ U(1)Q subgroup,

where SU(3)c describes the strong colour force amongst quarks holding the

Neutrinos in High Energy and Astroparticle Physics, First Edition. José W. F. Valle and Jorge C. Romão.© 2015 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2015 by Wiley-VCH Verlag GmbH & Co. KGaA.

2 1 Historical Introduction

Figure 1.1 Peter Higgs and Francois Englert shared the 2013 physics Nobel Prize for their

pioneering work on spontaneous symmetry-breaking in the standard model. Adapted from

the Wikimedia Commons

nucleus together, while U(1)Q describes the long-range electromagnetic force

between charged particles. The formulation of the spontaneous gauge symmetry-

breaking mechanism was pioneered by Englert, Brout, Higgs, Guralnik, Hagen

and Kibble (Figure 1.1) [15–17] and will be referred to in this book simply as

the Higgs mechanism. It implies the existence of a physical elementary scalar

particle, the so-called Higgs boson. Its recent discovery by the ATLAS and CMS

experiments at the Large Hadron Collider (LHC) at CERN [18–20] constitutes

an outstanding achievement in particle physics, and a triumph for elementary

particle theory, and was awarded the 2013 physics Nobel Prize. While the mass

∼ 125 GeV and current data on decay branching ratios seem, in general, to be

in accordance with expectations, a better understanding of its properties from

further data will be required in order to underpin the nature of the associated

dynamics and possibly uncover new principles in Nature.

Indeed, although recognized as an excellent approximation at energy scales

below a few hundred gigaelectronvolts (GeV) [21], the SU(3)c ⊗ SU(2)L ⊗ U(1)Ytheory is not believed to be the ultimate theory of elementary particle interac-

tions. For example, supersymmetry or strong dynamics has been suggested to

explain the naturalness of the electroweak breaking mechanism. The former [22,

23] is a symmetry that relates the SM states to a hypothetical set of supersym-

metric partners so that these cancel quadratically divergent contributions to

the Higgs squared-mass, ‘solving’ the so-called hierarchy problem. The new

states are odd under a new quantum number called R-parity, under which all

the SM particles are even. The so-called minimal supersymmetric standard

model (MSSM) assumes ad hoc conservation of R-parity [24]. In order to be

phenomenologically viable, supersymmetry must be broken in a way that is not

yet fully understood, but which should be ‘soft’ [25]. If sufficiently light, the states


corresponding to partners of the SM particles would be produced at the LHC,

current data already placing important restrictions on the model parameters.

While we eagerly wait for positive signs of new physics, such as supersymmetry,

in the next run of the LHC, we turn to the neutrino sector, which provides one of

the most solid present-day evidences for physics beyond the SM. Among the ele-

mentary building blocks of matter, neutrinos are unique in that they do not carry

an electric charge and as a result interact only weakly; hence their experimental

elusiveness. Neutrinos may pass through ordinary matter almost unaffected. As a

result, they constitute a unique probe of the very early Universe, and the precise

determination of their properties may hold the clue for what lies beyond the SM

of particle physics. Neutrinos come from ‘natural’ sources such as nuclear fusion

inside the Sun, cosmic ray interactions in the Earth’s atmosphere, the Earth’s nat-

ural radioactivity, supernova explosions, not to mention neutrinos produced pri-

mordially in the Big Bang itself.

There is one neutrino ‘flavour’ within each SM generation. The first neutrino νe

was discovered in nuclear reactors in 1956 [26], while the ν𝜇 [27] and the ν𝜏 [28]were discovered in particle accelerators in 1961 and 2000, respectively.Three neu-

trino species also fit well with the good measurement of the Z-boson ‘invisible’

width at LEP as well as with the primordial abundance of helium in the early Uni-

verse [29].

The Sun andmost visible stars produce their energy by the conversion of hydro-

gen to helium and are copious sources of neutrinos. Pontecorvo was the first to

speculate that such neutrinos might be detectable through radiochemical means

in a large volume of chlorine-bearing liquid [30]. In 1964, Bahcall andDavis argued

that a solar neutrino experiment would be feasible in a large enough detector

volume placed deep underground so as to reduce cosmic-ray-associated back-

grounds [31, 32]. In the late 1960s, Ray Davis proposed his pioneer geochemical

experiment at Homestake [33] , which captured fewer neutrinos than expected

in the standard solar model (Figure 1.2)( [34]). Understanding the observed solar

neutrino deficit remained a challenge until its final resolution over ten years ago,

which gave us irrefutable proof for the existence of neutrino mass, a possibility

always present ever since Pauli proposed the neutrino idea in order to account

for energy conservation in nuclear beta decays. However, the success of the V–A

hypothesis [35] in accounting for the observed parity violation in the weak inter-

action [36] was taken as an indication for massless neutrinos and incorporated

into the manifestly chiral formulation of the SU(3)c ⊗ SU(2)L ⊗ U(1)Y theory.

The 1980s saw a thriving period in neutrino physics. On the theory side,

motivated by the idea of grand unification [37–39], one started to question the

assumption of lepton (and baryon) number conservation [40]. The unification

idea inspired the seesaw mechanism as a way to understand the tiny neutrino

masses as resulting from the exchange of superheavy ‘messengers’, either fermions


(a) (b)

Figure 1.2 Ray Davis (a) and Masatoshi

Koshiba (b) (with C. K. Jung and C. Yanagi-

sawa) were recognized for their pioneering

contributions to astrophysics, including the

detection of solar and supernova neutrinos.

They shared the 2002 Nobel Prize with Ric-

cardo Giacconi for the discovery of X-ray

sources. Credit photo: Wikimedia Commons

(a) and courtesy of Chiaki Yanagisawa (b).

(type I) [41–47] or triplet scalars (type II seesaw) [46, 47].1) In order to describe

the phenomenology of neutrino oscillations, the multi-generation description

of the SU(3)c ⊗ SU(2)L ⊗ U(1)Y seesaw mechanism was formulated,2) leading to

the current form of the lepton mixing matrix, presented in terms of 1–2, 2–3

and 1–3 mixing angles 𝜃ij [46, 47, 58] as well as Dirac and Majorana CP phases

affecting oscillations and lepton number violation processes, respectively.3)

The last ingredient required in order to describe neutrino propagation was the

proper description of matter effects that are present in the interior of the Sun

or the Earth, formulated by Mikheev, Smirnov and Wolfenstein [59, 60]. On

the experimental front, the use of water Cherenkov detectors paved the way

to the historic detection of neutrinos from SN1987a in the Large Magellanic

Cloud [61–63]. Measurements of the zenith angle dependence and recoil energy

spectrum of solar neutrinos [64, 65] brought on a firmer observational basis the

long-standing problem of solar neutrinos indicated by geochemical experiments

since Homestake [33, 66–68]. Also, the observations of neutral current neutrino

interactions on deuterium at the Sudbury Neutrino Observatory (SNO) gave

strong evidence for solar νe flavour conversions [69], contributing also to the

determination of the oscillation parameters [70]. The ultimate elucidation of

the solar neutrino puzzle had to wait for the confirmation of the oscillation

hypothesis by the nuclear reactor experiment KamLAND. This experiment

1) Note that the seesaw ideawas first given in a phenomenological 𝜇 → e𝛾 paper [41], while in Ref. [46]

the suggested type I versus type II terminology was opposite to what became subsequently estab-

lished.2) This also led to low-scale seesaw realizations where messengers can be accessible to collider

searches [48–51] and also induce charged lepton flavour violation [52–54].3) The most general seesaw form of the lepton mixing matrix given in [46, 47] also describes a class

of non-standard neutrino conversion effects in matter [55–57].


measured not only the flux of νe’s from distant nuclear reactors in Japan but also

the spectrum distortion [71] matching the one expected from large mixing angle

oscillations. This was crucial to exclude non-standard solutions, thus establishing

robustness of large angle oscillations driven by 𝜃12 [72–74].

Cosmic ray interactions with atomic nuclei in the Earth’s atmosphere produces

particle showers, which end up in (anti)neutrinos. Large underground experi-

ments such as IMB,MACRO and Kamiokande-II indicated a deficit in the muon-

to-electron neutrino event ratio. The elucidation of this ‘anomaly’ had to wait till

the commissioning of the Super-K experiment, which gave a very high statistics

measurement over a wide energy range from hundreds of megaelectronvolts to a

few teraelectronvolts. It showed that the observed deficit in the𝜇-like atmospheric

events is due to ν𝜇 oscillations driven by 𝜃23 [75], a discovery later confirmed by

accelerator experiments such as K2K [76] and MINOS [77].

Recent reactor experiments, especially at Daya Bay, have observed the disap-

pearance of electron-anti-neutrinos at a distance of about 2 km from the reactors,

providing a robust determination of the third neutrinomixing angle, 𝜃13 [78], seen

also at accelerator experiments such as T2K [79]. This opens the door to a new

generation of oscillation experiments [80] probing CP violation in neutrino oscil-

lations [81], and may shed light on the mystery of flavour.

Note that in both solar and atmospheric ‘sectors’ there is independent confir-

mation of the oscillation hypothesis by experiments based at reactors and acceler-

ators. Neutrino oscillation physics is now a mature field brought to the precision

era. Dedicated fits [82, 83] indicate a pattern of mixing angles quite different from

the Cabibbo–Kobayashi–Maskawa (CKM) [84, 85] matrix which characterizes

quark mixing. Altogether, the discovery of neutrino oscillations constitutes a his-

toric landmark in particle physics, which not only implies new physics but is also

likely to pave the way for a deep understanding of the flavour puzzle. In particular,

lepton flavour violationmay also be seen in the charged lepton sector, irrespective

of neutrino mass, bringing complementary information [52–54, 86]. Moreover, it

is likely that there is total lepton number violation, as highlighted in the modern

gauge theoretical formulation of neutrinomasses. Proving theMajorana nature of

neutrinos requires searching for lepton number violation processes such as neu-

trinoless double beta decay [87, 88].

Further hints for new physics come from cosmology, which has made fast

progress over the last few years [89, 90]. Indeed, it is truly remarkable that< 5% of

the entire Universe consists of stuff we know, and all the rest remains a complete

mystery, dubbed dark matter and dark energy. As an example, we mention

dark matter, whose detailed nature remains elusive, despite strong evidence in

favour of its existence, ever since the pioneering observations of the astronomer

Fritz Zwicky in the 1930s. Dark matter neither emits nor scatters light or other

electromagnetic radiation, hence cannot be detected directly by optical or radio

astronomy. However, most of the mass in the Universe is indeed non-luminous,

and its existence is also inferred by the modelling of structure formation and

galaxy evolution. However, we still do not know its composition. Viable dark

matter particle physics candidates must be electrically neutral and provide the


correct relic abundance, hence they must be stable over cosmological time scales.

The most popular candidate is a weakly interacting massive particle (WIMP),

for example, the lightest supersymmetric particle in models with conserved

R-parity [91, 92].

Although neutrinos cannot provide the required dark matter, the physics

through which they acquire their small masses may be closely connected, provid-

ing a fascinating link between neutrinos and early Universe cosmology [93–96].

One interesting possibility is that dark matter is stabilized by a remnant of the

flavour symmetry which explains the oscillation pattern [97, 98]. Many other

types of relations between dark matter and neutrinos [99, 100] are considered

in Chapter 17. Another open issue in cosmology is the understanding of the

matter–antimatter asymmetry [101]. An attractive mechanism is to generate

a primordial lepton–anti-lepton asymmetry through the out-of-equilibrium

CP-violating decays of the messenger particles responsible for neutrino mass.

This would take place very early on in the evolution of the Universe, while

subsequent non-perturbative processes would convert the lepton number (B-L)

asymmetry into a baryon asymmetry. In such a leptogenesis picture, neutrinos

are responsible for the origin of matter.

To sum up, over the last century neutrinos have provided a crucial tool in our

understanding of weak interactions and guidance in the formulation of today’s SM

of particle physics. It is not risky to imagine that they may also help in directing

us towards the ‘theory of everything’ that lies ahead. Among the challenges in

present-day particle physics, many are coming from the neutrino sector. Some of

them are as follows:

1) The Nature of Neutrinos. Is lepton number violated in nature? Are neutrinos

their own anti-particles? The observation of neutrinoless double beta decay

(𝛽𝛽0ν) would provide the answer [87, 88] and many experiments are going

on [102–104].

2) The Origin of Neutrino Mass. Why are neutrinos so light when compared

the other elementary fermions? Is this a hint for some sort of unifica-

tion of the gauge interactions [37–39]? Are neutrino masses a low-scale

phenomenon? [48–51, 105–107]

3) The Pattern of Neutrino Mixing. Why are lepton mixing angles so differ-

ent from the CKM mixing angles? Is there an underlying symmetry of

flavour? [108–114]

4) Probing Non-standard Neutrino Interactions. Is there lepton flavour viola-

tion beyond that seen in oscillations? Do they show up in neutrino propa-

gation? [55–57, 115, 116]

5) Charged Lepton Flavour Violation and CP Violation. Do processes such as

𝜇 → e + 𝛾 take place? [117] Is leptonic CP violated? Does lepton flavour vio-

lation take place at LHC energies?This would be truly complementary to the

oscillation studies.

6) Probing Neutrinos at High Energy Accelerators. Can neutrino properties be

probed at LHC energies and higher? [118–122] Is teraelectronvolt-scale

supersymmetry the origin of neutrino mass? [123–126]

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