Three loop MSbar renormalization of QED in the 't~Hooft-Veltman gauge

TL;DR

This paper performs a three-loop renormalization of QED in the 't~Hooft-Veltman gauge within the MSbar scheme, calculating beta-functions and anomalous dimensions involving the gauge fixing parameter.

Contribution

It provides the first three-loop renormalization of QED in this specific nonlinear gauge, including the effects of an additional gauge parameter xi.

Findings

Beta-functions and anomalous dimensions computed at three loops.

Renormalization of the gauge parameter is singular, similar to QCD.

Results extend understanding of gauge fixing effects in QED.

Abstract

Quantum electrodynamics (QED) fixed in the 't~Hooft-Veltman gauge is renormalized to three loops in the MSbar scheme. The beta-functions and anomalous dimensions are computed as functions of the usual QED coupling and the additional coupling, xi, which is introduced as part of the nonlinear gauge fixing condition. Similar to the maximal abelian gauge of quantum chromodynamics, the renormalization of the gauge parameter is singular.