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

TL;DR

The paper develops an effective-field-theory framework to compute leading-logarithmic electroweak corrections to the muon anomalous magnetic moment $a_\mu$, using the renormalization-group evolution of a dipole operator $H_\mu$ and related four-fermion operators. It derives the two-loop LL result, confirms existing bosonic contributions, and provides the full $s_W^2$-dependent fermionic piece, then extends to the leading three-loop LL correction with a comprehensive operator basis; the combined LL results yield $a_\mu^{\rm EW}=(153\pm3)\times 10^{-11}$, with a small additional three-loop contribution of about $0.5\times 10^{-11}$. The authors also show how QED effects induce model-independent improvements for new-physics contributions to $a_\mu$ and to the electron EDM, reducing such effects by roughly 6% and 11% respectively for NP scales around the weak scale. Overall, the work provides a systematic, diagram-free method to capture large logarithms in electroweak corrections to dipole moments and demonstrates a general approach to assess NP effects in precision observables.

Abstract

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 θ_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).