QED Logarithms in the Electroweak Corrections to the Muon Anomalous Magnetic Moment

We employ an effective Lagrangian approach to derive the leading-logarithm two-loop electroweak contributions to the muon anomalous magnetic moment, a_mu. We show that these corrections can be obtained using known results on the anomalous dimensions of composite operators. We confirm the result of Czarnecki et al. for the bosonic part and present the complete sin^2 \theta_W dependence of the fermionic contribution. The approach is then used to compute the leading-logarithm three-loop electroweak contribution to a_mu. Finally we derive, in a fairly model-independent way, the QED improvement of new-physics contributions to a_mu and to the electric dipole moment (EDM) of the electron. We find that the QED corrections reduce the effect of new physics at the electroweak scale by 6% (for a_mu) and by 11% (for the electron EDM).