Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

TL;DR

This paper calculates four-loop light-by-light-type quantum electrodynamics corrections to the muon’s anomalous magnetic moment, confirming previous results through independent computational methods.

Contribution

It provides a novel four-loop calculation of light-by-light corrections to the muon g-2, using asymptotic expansion and integral reduction techniques.

Findings

Confirmed existing results with independent methods

Performed asymptotic expansion in electron-muon mass ratio

Evaluated master integrals analytically and numerically

Abstract

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider such corrections and present a calculation of the four-loop light-by-light-type corrections where the external photon couples to a closed electron or muon loop. We perform an asymptotic expansion in the ratio of electron and muon mass and reduce the resulting integrals to master integrals which we evaluate using analytical and numerical methods. We confirm the results present in the literature which are based on different computational methods.