Electron contribution to the muon anomalous magnetic moment at four loops

TL;DR

This paper calculates the four-loop quantum electrodynamics contributions to the muon's anomalous magnetic moment involving electron loops, providing precise analytic results and highlighting the significance of higher-order mass ratio terms.

Contribution

It presents the first complete four-loop electron-loop contribution to the muon g-2, including electron and tau loops, using asymptotic expansion methods.

Findings

Good numerical agreement with existing literature

Analytic results for three-loop muon mass and wave function renormalization constants

Highlights importance of higher order mass ratio terms

Abstract

We present results for the QED contributions to the anomalous magnetic moment of the muon containing closed electron loops. The main focus is on perturbative corrections at four-loop order where the external photon couples to the external muon. Furthermore, all four-loop contributions involving simultaneously a closed electron and tau loop are computed. In combination with our recent results on the light-by-light-type corrections (see Ref. \cite{Kurz:2015bia}) the complete four-loop electron-loop contribution to the anomalous magnetic moment of the muon has been obtained with an independent calculation. Our calculation is based on an asymptotic expansion in the ratio of the electron and the muon mass and shows the importance of higher order terms in this ratio. We perform a detailed comparison with results available in the literature and find good numerical agreement. As a by-product we present analytic results for the on-shell muon mass and wave function renormalization constants at three-loop order including massive closed electron and tau loops, which we also calculated using the method of asymptotic expansion.