Anomalous Magnetic Moment of the Electron, Muon, and Nucleon

The anomalous magnetic moment of the electron, 12(g-2), is computed using dispersion theory. The analytic continuation is made in the mass of one of the external electron lines and only the one-electron one-photon states are retained in the absorptive amplitude. In this way we relate g-2 to the Compton amplitude which has a known exact threshold behavior. Our approximation is an expansion in the low-energy behavior rather than a perturbation expansion in powers of 1/137, and we are able to show that a major contribution to g-2 comes from the low-mass region of the electron-photon system near the threshold of the absorptive amplitude. First, in a purely nonrelativistic calculation, we find that a major part of the α2π correction is accounted for by the Thomson limit. Further refining our calculation by including the exact residue of the pole terms in the Compton amplitude in accord with the low-energy theorem on Compton scattering, we find that electron-photon states below 2.5mc² in the absorptive amplitude reproduce 90% of the -0.328α²π² contribution and predict a value of ~+0.15α³π³ for the sixth-order term. We also give a simple physical interpretation of the difference of the muon and electron g-2 values. Finally we calculate with this approach the anomalous magnetic moments of the proton and neutron, with the Kroll-Ruderman theorem on meson photoproduction providing the low-energy "anchor" in this case. Again retaining only the low-mass region of the absorptive amplitude, we obtain fair agreement with the magnitude and the isovector character of the moments, finding Δμ^P~0.7(Δμ_expt) and Δμ^N~0.9(Δμ_expt).