1 Introduction .................................................. 1
1.1 Preliminary Remarks ....................................... 1
1.2 Muon Spin Precession in the Storage Ring .................. 4
References .................................................... 6
2 QED Effects in the Muon Magnetic Anomaly ...................... 7
2.1 General Considerations .................................... 7
2.2 Features of the Radiative Corrections to the Muon
Magnetic Anomaly ......................................... 10
2.3 One-loop QED Contribution: Schwinger Correction .......... 12
2.4 Two-loop QED Corrections to aμ ........................... 17
2.5 Three-loop QED Corrections to aμ ......................... 25
2.6 Four- and Five-loop QED Corrections ...................... 29
2.7 Complete QED Contribution to the Muon Magnetic Anomaly ... 31
References ................................................... 31
3 Hadronic Vacuum Polarization ................................. 33
3.1 Hadronic Vacuum Polarization: The Basics ................. 33
3.2 Theoretical Methods ...................................... 35
3.2.1 Large-Nc Approximation in QCD ...................... 35
3.2.2 The Operator Product Expansion ..................... 38
3.2.3 An Example: The Charged-neutral Pion Mass
Difference ......................................... 46
3.3 Hadronic Vacuum Polarization: The Theoretical Estimate ... 48
3.4 Basics of the Data-driven Analysis ....................... 52
3.4.1 Preliminary Remarks ................................ 52
3.4.2 Theoretical Issues ................................. 55
3.4.3 Combining the Data ................................. 57
3.4.4 Specific Contributions to the Convolution
Integral ........................................... 59
3.4.5 The Two-pion Channel ............................... 61
3.4.6 Comparative Analysis ............................... 63
3.4.7 Final Remarks ...................................... 65
3.5 Hadronic Vacuum Polarization: Inclusion of the τ-data .... 65
3.6 Hadronic Vacuum Polarization:
The τ Data and the Isospin Symmetry Violations ........... 69
3.7 Higher Order QED Corrections to Hadronic Vacuum
Polarization Contribution to aμ .......................... 83
3.8 Total Hadronic Vacuum Polarization Contribution .......... 84
References ................................................... 85
4 Electroweak Corrections to aμ ................................ 89
4.1 Weak Corrections to aμ ................................... 89
4.2 Two-loop Electroweak Effects: The Logarithmic
Approximation ............................................ 91
4.2.1 Effective Field Theory ............................. 91
4.2.2 Anomalous Dimension and Mixing of Effective
Operators .......................................... 94
4.2.3 Mixing of Four-fermion Operators; Triangle
Diagrams ........................................... 95
4.2.4 The Two-loop Electroweak Correction ............... 101
References .................................................. 102
5 Strong Interaction Effects in Electroweak Corrections ....... 103
5.1 Anomalous Quark Triangles: Effects of Strong
Interactions ............................................ 103
5.1.1 Perturbative Calculations ......................... 105
5.1.2 Non-perturbative Effects and the OPE .............. 108
5.1.3 Models of the Structure Functions ................. 114
5.2 Final Results for the Electroweak Corrections ........... 119
References .................................................... 120
6 Hadronic Light-by-light Scattering and the Muon Magnetic
Anomaly ..................................................... 121
6.1 Calculating the Hadronic Light-by-light Scattering
Contribution: An Overview ............................... 122
6.2 The Light-by-light Scattering Contribution to the Muon
Anomaly in QED .......................................... 124
6.3 Hadronic Light-by-light Scattering: Logarithmic Terms ... 126
6.4 Model for the Hadronic Light-by-light Scattering ........ 130
6.4.1 Operator Product Expansion and Triangle
Amplitude ......................................... 130
6.4.2 The Model ......................................... 133
6.5 Constraints on the Pseudoscalar Exchange ................ 134
6.6 Pseudovector Exchange ................................... 137
6.7 The Pion Box Contribution ............................... 140
6.8 The Hadronic Light-by-light Scattering Contribution to
aμ ...................................................... 143
References .................................................. 144
7 Standard Model Value for the Muon Magnetic Anomaly .......... 145
References .................................................. 149
8 New Physics and the Muon Anomalous Magnetic Moment .......... 151
8.1 Supersymmetry ........................................... 152
8.1.1 The Anomalous Magnetic Moment in Supersymmetric
QED ............................................... 152
8.1.2 Supersymmetric Extensions of the Standard Model ... 155
8.2 Additional Vector Bosons ................................ 161
8.3 Compositeness of the Standard Model Gauge Bosons ........ 162
8.4 Extensions of the Higgs Sector .......................... 163
8.5 Extra Dimensions ........................................ 166
References .................................................. 168
Summary ..................................................... 171
References .................................................. 172
Appendix .................................................... 173
A.1 Notation ................................................ 173
A.2 Gounaris-Sakurai Parametrization of the Pion Form
Factor .................................................. 173
References .................................................. 174
Index ......................................................... 175
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