Preprint[pdf] - HU Berlin

Contents
1 Introduction 2
1.1 History 6
1.2 Muon Properties 8
1.3 Lepton Magnetic Moments 11
2 The Muon g − 2 Experiments 13
2.1 The Brookhaven Muon g − 2 Experiment 13
2.2 Summary of Experimental Results 18
3 QED Prediction of g − 2 19
3.1 Universal Contributions 21
3.2 Electron Anomalous Magnetic Moment and the Fine Structure Constant 25
3.3 Mass Dependent Contributions 27
4 Hadronic Vacuum Polarization Corrections 38
4.1 Lowest Order Vacuum Polarization Contribution 40
4.2 Higher Order Hadronic Vacuum Polarization Corrections 52
5 Hadronic Light-by-Light Scattering Contribution 56
5.1 Pseudoscalar–exchange Contribution 61
5.2 Summary of the Light-by-Light Scattering Results 73
5.3 An Effective Field Theory Approach to Hadronic Light-by-Light Scattering 78
6 Electroweak Corrections 80
6.1 1-loop Contribution 80
6.2 2-loop Contribution 81
6.3 2–loop electroweak contributions to ae 93
7 Muon g-2: Theory versus Experiment 95
7.1 Standard Model Prediction 95
7.2 New Physics Contributions 97
8 Outlook and Conclusions 119
8.1 Future Experimental Possibilities 119
8.2 Theory: Critical Assessment of Theoretical Errors and Open Problems 120
8.3 Conclusions 123
A Some Standard Model parameters, ζ values and polylogarithms 124
References 126
1. Introduction
The electron’s spin and magnetic moment were evidenced from the deflection of atoms in an inhomogeneous
magnetic field and the observation of the fine structure by optical spectroscopy [1,2]. Ever since, magnetic
moments and g–values of particles in general and the g − 2 experiments with the electron and the muon
in particular, together with high precision atomic spectroscopy, have played a central role in establishing
the modern theoretical framework for particle physics. That is relativistic quantum field theory in general
and quantum electrodynamics in particular, the prototype theory which developed further into the so called
“Standard Model” (SM) of electromagnetic, weak and strong interactions based on a local gauge principle
and spontaneous symmetry breaking. The muon g −2 is one of the most precisely measured and theoretically
best investigated quantities in particle physics. Our interest in very high precision measurements is motivated
by our eagerness to exploit the limits of our present understanding of nature and to find effects which cannot
be explained by the established theory. More than 30 years after its invention this is still the SM of elementary
particle interactions, a SU(3)c ⊗ SU(2)L ⊗ U(1)Y gauge theory broken to SU(3)c ⊗ U(1)em by the Higgs
mechanism, which requires a not yet discovered Higgs particle to exist.
Designed to be a local, causal and renormalizable quantum field theory, quarks and leptons are allowed
to come only in families in order to be anomaly free and not to conflict with renormalizability. So we have
as the first family the quark doublet (u, d) of the up and down quarks accompanied by the lepton doublet
(νe, e − ) with the electron neutrino and the electron, with the left-handed fields in the doublets and all their
right-handed partners in singlets. All normal matter is made up from these 1st family fermions.
Most surprisingly a second and even a third quark–lepton family exist in nature, all with identical quantum
numbers, as if nature would repeat itself. The corresponding members in the different families only differ
by their mass where the mass scales span an incredible range, from mνe < ∼ 10−3 eV for the electron neutrino
2