Gauge Theories of the Strong, Weak, and Electromagnetic Interactions

Preface xi

One Introduction 1

1.1 Elements of the Standard Model of Particle Physics 4

1.2 Leptons 6

1.3 Quarks 7

1.4 The Fundamental Interactions 15

Problems 18

For Further Reading 21

References 23

Two Lagrangian Formalism and Conservation Laws 25

2.1 Hamilton's Principle 26

2.2 Free Field Theory Examples 28

2.3 Symmetries and Conservation Laws 30

Problems 33

For Further Reading 35

References 37

Three The Idea of Gauge Invariance 38

3.1 Historical Preliminaries 38

3.2 Gauge Invariance in Classical Electrodynamics 40

3.3 Phase Invariance in Quantum Mechanics 42

3.4 Significance of Potentials in Quantum Theory 44

3.5 Phase Invariance in Field Theory 46

3.6 Feynman Rules for Electromagnetism 50

Problems 52

For Further Reading 53

References 56

Four Non-Abelian Gauge Theories 57

4.1 Motivation 57

4.2 Construction 58

4.3 Some Physical Consequences 63

4.4 Assessment 66

Problems 66

For Further Reading 69

References 70

Five Hidden Symmetries 71

5.1 The Idea of Spontaneously Broken Symmetries 72

5.2 Spontaneous Breaking of Continuous Symmetries 76

5.3 Spontaneous Breaking of a Gauge Symmetry 78

5.4 The Sigma Model 81

5.5 Spontaneous Breaking of a Non-Abelian Symmetry 86

5.6 Prospects 87

Problems 88

For Further Reading 91

References 94

Six Electroweak Interactions of Leptons 95

6.1 An Effective Lagrangian for the Weak Interactions 96

6.2 Intermediate Vector Bosons: A First Look 110

6.3 The Standard Electroweak Theory of Leptons 120

6.4 Neutral-Current Interactions among Leptons 135

6.5 The Higgs Boson: A First Look 146

6.6 The Higgs Boson, Asymptotic Behavior, and the 1-TeV Scale 151

6.7 Neutrino Mixing and Neutrino Mass 156

6.8 Renormalizability of the Theory 166

6.9 Interim Assessment 170

Problems 171

For Further Reading 177

References 183

Seven Electroweak Interactions of Quarks 187

7.1 The Standard Electroweak Theory: Preliminaries 188

7.2 Electroweak Gauge Bosons 194

7.3 Electron-Positron Annihilations 198

7.4 Deeply Inelastic Lepton-Hadron Scattering 205

7.5 Hadron-Hadron Interactions 223

7.6 Further Tests of the Electroweak Theory 229

7.7 A Brief Look at Quantum Corrections 231

7.8 The Scale of Fermion Masses 236

7.9 Search for the Higgs Boson 237

7.10 Incompleteness of the Electroweak Theory 241

7.11 The Hierarchy Problem 244

7.12 The Vacuum Energy Problem 246

7.13 Reflections 247

Problems 249

For Further Reading 258

References 263

Eight Strong Interactions among Quarks 269

8.1 A Color Gauge Theory 270

8.2 Charge Renormalization in Electrodynamics 281

8.3 The Running Coupling Constant in QCD 294

8.4 Perturbative QCD: A First Example 303

8.5 QCD Corrections to Deeply Inelastic Scattering 308

8.6 Jets in Hadron-Hadron Collisions 325

8.7 Two-Photon Processes and the Photon-Structure Function 328

8.8 Color Confinement 336

8.9 QCD-induced Electroweak Symmetry Breaking 341

8.10 The 1/N Expansion 345

8.11 Strong-Interaction Symmetries 352

8.12 Assessment 356

Problems 358

For Further Reading 369

References 381

Nine Unified Theories 387

9.1 Why Unify? 389

9.2 The SU(5) Model 391

9.3 Coupling-Constant Unification 402

9.4 Nucleon Decay 408

9.5 The Baryon Number of the Universe 410

9.6 The Problem of Fermion Masses 414

9.7 Assessment 416

Problems 418

For Further Reading 423

References 427

Epilogue 430

Appendix A Notations and Conventions 433

A.1 Four-Vectors and Scalar Product 433

A.2 Dirac Matrices 434

A.3 Trace Theorems and Tensor Contractions 436

A.4 Dirac Equation and Dirac Spinors 437

A.5 Color Algebra 440

A.6 Weyl-van der Waerden Spinors 444

References 445

Appendix B Observables and Feynman Rules 447

B.1 Phase-Space Formulas: Decay Rates and Cross Sections 447

B.2 Feynman Rules: Generalities 448

B.3 Feynman Integrals 450

B.4 Regularization Procedures 452

B.5 Feynman Rules: Electrodynamics 453

For Further Reading 454

References 456

Appendix C Physical Constants 457

For Further Reading 457

Author Index 459

Subject Index 475