Three loop MSbar renormalization of QCD in the maximal abelian gauge

TL;DR

This paper computes three-loop anomalous dimensions in QCD within the maximal abelian gauge, providing detailed renormalization group functions and exploring their relation to other gauges.

Contribution

It presents the first three-loop MSbar renormalization of various fields and parameters in QCD for an arbitrary gauge group in the maximal abelian gauge.

Findings

Three-loop anomalous dimensions for quarks, gluons, ghosts, and gauge parameters.

Connection between maximal abelian gauge and Curci-Ferrari gauge in certain limits.

Derivation of the anomalous dimension of the BRST invariant mass operator.

Abstract

We determine the three loop anomalous dimensions of the quark, centre and off-diagonal gluons, centre and off-diagonal ghosts and the gauge fixing parameters in the maximal abelian gauge for an arbitrary colour group in the MSbar renormalization scheme at three loops. We show that the three loop MSbar beta-function emerges from the renormalization of the centre gluon and also deduce the anomalous dimension of the BRST invariant dimension two mass operator. Moreover, we demonstrate that in the limit that the dimension of the centre of the group tends to zero, the anomalous dimensions of the quarks, off-diagonal gluons and off-diagonal ghosts tend to those of the quarks, gluons and ghosts of the Curci-Ferrari gauge respectively.