Theory of the Anomalous Magnetic Moment of the Electron

The anomalous magnetic moment of the electron ae measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant alpha, with an effective parameter alpha/pi. Both numerical and analytic evaluations of ae up to (alpha/pi)4 are firmly established. The coefficient of (alpha/pi)5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to ae(theory) = 1159652181.606(11)(12)(229)x10-12, where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: alpha-1(Cs)=137.035999046(27). The discrepancy between ae(theory) and ae((experiment)) is 2.4 sigma. Assuming that the standard model is valid so that ae(theory) = ae(experiment) holds, we obtain alpha-1(ae)=137.0359991496(13)(14)(330), which is nearly as accurate as alpha-1(Cs). The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of ae, in this order.