Introduction to Elementary Particles, 2nd, Revised Edition

Preface to the First Edition ix

Preface to the Second Edition xi

Formulas and Constants xiii

Introduction 1

1 Historical Introduction to the Elementary Particles 13

1.1 The Classical ERA (1897–1932) 13

1.2 The Photon (1900–1924) 15

1.3 Mesons (1934–1947) 18

1.4 Antiparticles (1930–1956) 20

1.5 Neutrinos (1930–1962) 23

1.6 Strange Particles (1947–1960) 30

1.7 The Eightfold Way (1961–1964) 35

1.8 The Quark Model (1964) 37

1.9 The November Revolution and Its Aftermath (1974–1983 and 1995) 44

1.10 Intermediate Vector Bosons (1983) 47

1.11 The Standard Model (1978–?) 49

2 Elementary Particle Dynamics 59

2.1 The Four Forces 59

2.2 Quantum Electrodynamics (QED) 60

2.3 Quantum Chromodynamics (QCD) 66

2.4 Weak Interactions 71

2.4.1 Neutral 72

2.4.2 Charged 74

2.4.2.1 Leptons 74

2.4.2.2 Quarks 75

2.4.3 Weak and Electromagnetic Couplings of W and Z 78

2.5 Decays and Conservation Laws 79

2.6 Unification Schemes 84

3 Relativistic Kinematics 89

3.1 Lorentz Transformations 89

3.2 Four-vectors 92

3.3 Energy and Momentum 96

3.4 Collisions 100

3.4.1 Classical Collisions 100

3.4.2 Relativistic Collisions 101

3.5 Examples and Applications 102

4 Symmetries 115

4.1 Symmetries, Groups, and Conservation Laws 115

4.2 Angular Momentum 120

4.2.1 Addition of Angular Momenta 122

4.2.2 Spin 1/2 125

4.3 Flavor Symmetries 129

4.4 Discrete Symmetries 136

4.4.1 Parity 136

4.4.2 Charge Conjugation 142

4.4.3 CP 144

4.4.3.1 Neutral Kaons 145

4.4.3.2 CP Violation 147

4.4.4 Time Reversal and the TCP Theorem 149

5 Bound States 159

5.1 The Schrödinger Equation 159

5.2 Hydrogen 162

5.2.1 Fine Structure 165

5.2.2 The Lamb Shift 166

5.2.3 Hyperfine Splitting 167

5.3 Positronium 169

5.4 Quarkonium 171

5.4.1 Charmonium 174

5.4.2 Bottomonium 175

5.5 Light Quark Mesons 176

5.6 Baryons 180

5.6.1 Baryon Wave Functions 181

5.6.2 Magnetic Moments 189

5.6.3 Masses 191

6 The Feynman Calculus 197

6.1 Decays and Scattering 197

6.1.1 Decay Rates 197

6.1.2 Cross Sections 199

6.2 The Golden Rule 203

6.2.1 Golden Rule for Decays 204

6.2.1.1 Two-particle Decays 206

6.2.2 Golden Rule for Scattering 208

6.2.2.1 Two-body Scattering in the CM Frame 209

6.3 Feynman Rules for a Toy Theory 211

6.3.1 Lifetime of the A 214

6.3.2 A + A → B + B Scattering 215

6.3.3 Higher-order Diagrams 217

7 Quantum Electrodynamics 225

7.1 The Dirac Equation 225

7.2 Solutions to the Dirac Equation 229

7.3 Bilinear Covariants 235

7.4 The Photon 238

7.5 The Feynman Rules for QED 241

7.6 Examples 245

7.7 Casimir’s Trick 249

7.8 Cross Sections and Lifetimes 254

7.9 Renormalization 262

8 Electrodynamics and Chromodynamics of Quarks 275

8.1 Hadron Production in e⁺e⁻ Collisions 275

8.2 Elastic Electron–Proton Scattering 279

8.3 Feynman Rules For Chromodynamics 283

8.4 Color Factors 289

8.4.1 Quark and Antiquark 289

8.4.2 Quark and Quark 292

8.5 Pair Annihilation in QCD 294

8.6 Asymptotic Freedom 298

9 Weak Interactions 307

9.1 Charged Leptonic Weak Interactions 307

9.2 Decay of the Muon 310

9.3 Decay of the Neutron 315

9.4 Decay of the Pion 321

9.5 Charged Weak Interactions of Quarks 324

9.6 Neutral Weak Interactions 329

9.7 Electroweak Unification 338

9.7.1 Chiral Fermion States 338

9.7.2 Weak Isospin and Hypercharge 342

9.7.3 Electroweak Mixing 345

10 Gauge Theories 353

10.1 Lagrangian Formulation of Classical Particle Mechanics 353

10.2 Lagrangians in Relativistic Field Theory 354

10.3 Local Gauge Invariance 358

10.4 Yang–Mills Theory 361

10.5 Chromodynamics 366

10.6 Feynman Rules 369

10.7 The Mass Term 372

10.8 Spontaneous Symmetry-breaking 375

10.9 The Higgs Mechanism 378

11 Neutrino Oscillations 387

11.1 The Solar Neutrino Problem 387

11.2 Oscillations 390

11.3 Confirmation 392

11.4 Neutrino Masses 395

11.5 The Mixing Matrix 397

12 Afterword: What’s Next? 401

12.1 The Higgs Boson 401

12.2 Grand Unification 405

12.3 Matter/Antimatter Asymmetry 409

12.4 Supersymmetry, Strings, Extra Dimensions 411

12.4.1 Supersymmetry 411

12.4.2 Strings 413

12.5 Dark Matter/Dark Energy 414

12.5.1 Dark Matter 414

12.5.2 Dark Energy 416

12.6 Conclusion 417

A The Dirac Delta Function 423

B Decay Rates and Cross Sections 429

B.1 Decays 429

B.1.1 Two-body Decays 429

B.2 Cross Sections 430

B.2.1 Two-body Scattering 430

C Pauli and Dirac Matrices 433

C.1 Pauli Matrices 433

C.2 Dirac Matrices 434

D Feynman Rules (Tree Level) 437

D.1 External Lines 437

D.2 Propagators 437

D.3 Vertex Factors 438

Index 441