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Part I Basic Concepts, Introduction to QED, g - 2 in a Nutshell, General Properties and Tools |
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3 | (20) |
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18 | (5) |
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2 Quantum Field Theory and Quantum Electrodynamics |
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23 | (140) |
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2.1 Quantum Field Theory Background |
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23 | (13) |
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2.1.1 Concepts, Conventions and Notation |
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23 | (8) |
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31 | (5) |
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36 | (11) |
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2.3 Quantum Electrodynamics |
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47 | (13) |
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2.3.1 Perturbation Expansion, Feynman Rules |
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50 | (5) |
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2.3.2 Transition Matrix--Elements, Particle--Antiparticle Crossing |
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55 | (3) |
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2.3.3 Cross Sections and Decay Rates |
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58 | (2) |
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2.4 Regularization and Renormalization |
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60 | (11) |
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2.4.1 The Structure of the Renormalization Procedure |
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60 | (4) |
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2.4.2 Dimensional Regularization |
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64 | (7) |
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2.5 Tools for the Evaluation of Feynman Integrals |
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71 | (20) |
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2.5.1 ε = 4 - d Expansion, ε → + 0 |
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71 | (1) |
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2.5.2 Bogolubov--Schwinger Parametrization |
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72 | (1) |
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2.5.3 Feynman Parametric Representation |
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73 | (1) |
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2.5.4 Euclidean Region, Wick--Rotations |
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73 | (3) |
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2.5.5 The Origin of Analyticity |
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76 | (9) |
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2.5.6 Scalar One--Loop Integrals |
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85 | (3) |
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88 | (3) |
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2.6 One--Loop Renormalization |
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91 | (52) |
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2.6.1 The Photon Propagator and the Photon Self--Energy |
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91 | (10) |
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2.6.2 The Electron Self--Energy |
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101 | (7) |
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2.6.3 Charge Renormalization |
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108 | (9) |
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2.6.4 Dyson-- and Weinberg--Power-Counting Theorems |
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117 | (3) |
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2.6.5 The Running Charge and the Renormalization Group |
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120 | (11) |
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2.6.6 Bremsstrahlung and the Bloch--Nordsieck Prescription |
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131 | (12) |
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2.7 Pions in Scalar QED and Vacuum Polarization by Vector Mesons |
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143 | (5) |
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2.8 Note on QCD: The Feynman Rules and the Renormalization Group |
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148 | (15) |
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158 | (5) |
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3 Lepton Magnetic Moments: Basics |
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163 | (86) |
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3.1 Equation of Motion for a Lepton in an External Field |
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163 | (5) |
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3.2 Magnetic Moments and Electromagnetic Form Factors |
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168 | (33) |
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3.2.1 Main Features: An Overview |
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168 | (25) |
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3.2.2 The Anomalous Magnetic Moment of the Electron |
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193 | (6) |
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3.2.3 The Anomalous Magnetic Moment of the Muon |
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199 | (2) |
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3.3 Structure of the Electromagnetic Vertex in the SM |
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201 | (4) |
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3.4 Dipole Moments in the Non--Relativistic Limit |
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205 | (2) |
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207 | (6) |
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3.6 Properties of the Form Factors |
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213 | (1) |
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214 | (12) |
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3.7.1 Dispersion Relations and the Vacuum Polarization |
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216 | (10) |
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3.8 Dispersive Calculation of Feynman Diagrams |
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226 | (10) |
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3.9 ζ - Values, Polylogarithms and Related Special Functions |
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236 | (13) |
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241 | (8) |
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Part II A Detailed Account of the Theory, Outline of Concepts of the Experiment, Status and Perspectives |
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4 Electromagnetic and Weak Radiative Corrections |
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249 | (94) |
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4.1 g - 2 in Quantum Electrodynamics |
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249 | (38) |
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4.1.1 One--Loop QED Contribution |
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251 | (1) |
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4.1.2 Two--Loop QED Contribution |
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252 | (3) |
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4.1.3 Three--Loop QED Contribution |
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255 | (6) |
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4.1.4 Four--Loop QED Contribution |
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261 | (9) |
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4.1.5 Five--Loop QED Contribution |
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270 | (3) |
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4.1.6 Four- and Five--Loop Analytic Results and Crosschecks |
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273 | (14) |
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287 | (56) |
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4.2.1 Weak One--Loop Effects |
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294 | (1) |
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4.2.2 Weak Two--Loop Effects |
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295 | (39) |
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4.2.3 Two--Loop Electroweak Contributions to ae |
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334 | (3) |
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337 | (6) |
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343 | (228) |
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5.1 Hadronic Vacuum Polarization |
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345 | (84) |
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5.1.1 Vacuum Polarization Effects and e + e- Data |
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345 | (11) |
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5.1.2 Integrating the Experimental Data and Estimating the Error |
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356 | (4) |
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5.1.3 The Cross-Section e+ e- → Hadrons |
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360 | (4) |
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5.1.4 Photon Vacuum Polarization and the Complex αQED(s) |
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364 | (5) |
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5.1.5 R(s) in Perturbative QCD |
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369 | (5) |
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5.1.6 Non--Perturbative Effects, Operator Product Expansion |
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374 | (3) |
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5.1.7 Leading Hadronic Contribution to (g - 2) of the Muon |
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377 | (15) |
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5.1.8 Addendum I: The Hadronic Contribution to the Running Fine Structure Constant |
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392 | (4) |
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5.1.9 Addendum II: The Hadronic Contribution to the Running SU(2)L Gauge Coupling |
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396 | (4) |
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5.1.10 Addendum III: τ Spectral Functions versus e+ e- Annihilation Data |
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400 | (2) |
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5.1.11 A Minimal Model: VMD + sQED Resolving the τ versus e+ e- Puzzle |
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402 | (18) |
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5.1.12 Hadronic Higher Order Contributions |
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420 | (7) |
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5.1.13 Next-to-Next Leading Order Hadronic Contributions |
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427 | (2) |
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5.2 Hadronic Light--by--Light Scattering |
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429 | (99) |
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5.2.1 Calculating the Hadronic LbL Contribution |
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434 | (4) |
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5.2.2 Sketch on Hadronic Models |
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438 | (7) |
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5.2.3 Pion--Exchange Contribution |
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445 | (5) |
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5.2.4 The π0γγ Transition Form Factor |
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450 | (37) |
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5.2.5 Exchanges of Axial-Vector Mesons |
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487 | (6) |
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5.2.6 Exchanges of Scalar Mesons |
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493 | (3) |
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496 | (1) |
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497 | (4) |
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501 | (2) |
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5.2.10 A Summary of Results |
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503 | (3) |
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5.2.11 The Dispersive Approach |
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506 | (22) |
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528 | (43) |
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5.3.1 Lattice QCD Approach to HVP |
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535 | (15) |
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5.3.2 Lattice QCD Approach to HLbL |
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550 | (8) |
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558 | (13) |
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571 | (38) |
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6.1 Overview on the Principle of the Experiment |
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571 | (6) |
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577 | (3) |
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6.3 Magnetic Precession for Moving Particles |
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580 | (7) |
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6.3.1 g - 2 Experiment and Magic Momentum |
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582 | (5) |
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6.4 Theory: Production and Decay of Muons |
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587 | (8) |
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595 | (2) |
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6.6 Ground State Hyperfine Structure of Muonium |
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597 | (2) |
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6.7 Single Electron Dynamics and the Electron g - 2 |
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599 | (4) |
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6.8 The Upcoming Experiments: What Is New? |
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603 | (6) |
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606 | (3) |
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7 Comparison Between Theory and Experiment and Future Perspectives |
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609 | (74) |
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7.1 Experimental Results Confront Standard Theory |
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609 | (5) |
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614 | (50) |
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7.2.1 Generic Contributions from Physics Beyond the SM |
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621 | (5) |
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7.2.2 Flavor Changing Processes |
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626 | (2) |
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7.2.3 Anomalous Couplings |
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628 | (1) |
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7.2.4 Two-Higgs Doublet Models |
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629 | (10) |
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639 | (22) |
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7.2.6 Dark Photon/Z and Axion Like Particles |
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661 | (3) |
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7.3 Outlook on the Upcoming Experiments |
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664 | (1) |
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7.4 Perspectives for the Future |
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665 | (18) |
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674 | (9) |
Appendix A List of Acronyms |
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683 | (4) |
Index |
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687 | |