The Anomalous Magnetic Moment of the Muon (Springer Tracts in Modern Physics, 226)

The Anomalous Magnetic Moment of the Muon, Springer Tracts in Modern Physics Volume 226......Page 1
Springer Tracts in Modern Physics......Page 3
Title Page......Page 4
Copyright
......Page 5
Preface......Page 8
Contents......Page 12
Part I Basic Concepts, Introduction to QED, g – 2 in a Nutshell, General Properties and Tools......Page 15
1 Introduction......Page 17
2.1.1 Concepts, Conventions and Notation......Page 37
2.1.2 C, P, T and CPT......Page 44
2.2 The Origin of Spin......Page 48
2.3 Quantum Electrodynamics......Page 58
2.3.1 Perturbation Expansion, Feynman Rules......Page 60
2.3.2 Transition Matrix–Elements, Particle–Antiparticle Crossing......Page 65
2.3.3 Cross Sections and Decay Rates......Page 67
2.4.1 The Structure of the Renormalization Procedure......Page 69
2.4.2 Dimensional Regularization......Page 72
2.5.1   = 4− d Expansion,   → +0......Page 79
2.5.3 Feynman Parametric Representation......Page 80
2.5.4 Euclidean Region, Wick–Rotations......Page 81
2.5.5 The Origin of Analyticity......Page 83
2.5.6 Scalar One–Loop Integrals......Page 86
2.5.7 Tensor Integrals......Page 88
2.6.1 The Photon Propagator and the Photon Self–Energy......Page 90
2.6.2 The Electron Self–Energy......Page 100
2.6.3 Charge Renormalization......Page 106
2.6.4 Dyson– and Weinberg–Power-Counting Theorems......Page 114
2.6.5 The Running Charge and the Renormalization Group......Page 116
1) UV behavior......Page 121
2) IR behavior......Page 123
2.6.6 Bremsstrahlung and the Bloch-Nordsieck Prescription......Page 126
2.7 Pions in Scalar QED and Vacuum Polarization by Vector Mesons......Page 135
2.8 Note on QCD: The Feynman Rules and the Renormalization Group......Page 139
3.1EquationofMotionforaLeptoninanExternalField......Page 149
3.2.1 Main Features: An Overview......Page 154
1) QED universal part:......Page 160
2) QED mass dependent part:......Page 162
3) Hadronic VP Effects:......Page 167
4) Hadronic LbL Effects:......Page 171
5) Weak interaction corrections:......Page 174
3.2.2 The Anomalous Magnetic Moment of the Electron......Page 176
3.2.3 The Anomalous Magnetic Moment of the Muon......Page 180
3.3 Structure of the Electromagnetic Vertex in the SM......Page 182
3.4 Dipole Moments in the Non–Relativistic Limit......Page 186
3.5 Projection Technique......Page 187
3.6 Properties of the Form Factors......Page 193
3.7 Dispersion Relations......Page 195
3.7.1 Dispersion Relations and the Vacuum Polarization......Page 196
3.8 Dispersive Calculation of Feynman Diagrams......Page 204
Part II A Detailed Account of the Theory, Outline of Concepts of the Experiment, Status and Perspectives......Page 219
4.1 g − 2 in Quantum Electrodynamics......Page 221
4.1.2 Two–Loop QED Contribution......Page 223
4.1.3 Three–Loop QED Contribution......Page 227
4.1.4 Four–Loop QED Contribution......Page 232
4.1.5 Five–Loop QED Contribution......Page 236
4.2 Weak Contributions......Page 238
4.2.1 Weak One–Loop Effects......Page 242
4.2.2 Weak Two–Loop Effects......Page 243
5 Hadronic Effects......Page 277
5.1 Vacuum Polarization Effects and......Page 278
5.1.1 Integrating the Experimental Data and Estimating the Error......Page 289
5.1.2 The Cross–Section......Page 291
5.1.3 R(s) in Perturbative QCD......Page 296
5.1.4 Non–Perturbative Effects, Operator Product Expansion......Page 300
5.2 Leading Hadronic Contribution to to (g − 2) of the Muon......Page 303
5.2.1 Addendum I: The Hadronic Contribution to the Running Fine Structure Constant......Page 309
5.2.2 Addendum II: τ Spectral Functions 
vs. e+e− Annihilation Data......Page 310
5.2.3 Digression: Exercises on the Low Energy Contribution......Page 312
5.3 Higher Order Contributions......Page 318
5.4 Hadronic Light–by–Light Scattering......Page 324
5.4.1 Calculating the Hadronic LbL Contribution......Page 328
5.4.2 Sketch on Hadronic Models......Page 330
5.4.3 Pion–pole Contribution......Page 337
5.4.4 The π0γγ Transition Form Factor......Page 339
5.4.5 A Summary of Results......Page 351
6.1 Overview on the Principle of the Experiment......Page 361
6.2 Particle Dynamics......Page 366
6.3 Magnetic Precession for Moving Particles......Page 369
6.3.1 g − 2 Experiment and Magic Momentum......Page 372
6.4 Theory: Production and Decay of Muons......Page 376
6.5 Muon g −2 Results......Page 379
6.6 Ground State Hyper.ne Structure of Muonium......Page 381
6.7 Single Electron Dynamics and the Electron......Page 383
7.1 Experimental Results Confront Standard Theory......Page 389
7.2 New Physics in g − 2......Page 395
7.2.1 Anomalous Couplings......Page 406
7.2.2 Supersymmetry......Page 407
7.3 Perspectives for the Future......Page 420
List of Acronyms......Page 429
Index......Page 435