Three loop MSbar anomalous dimension for renormalizable gauge invariant non-local gluon mass operator in QCD

TL;DR

This paper calculates the three-loop anomalous dimension of a gauge-invariant, non-local gluon mass operator in QCD within the MSbar scheme, confirming consistency with the known QCD beta-function.

Contribution

It provides the first three-loop calculation of the anomalous dimension for a non-local gluon mass operator and related ghost fields in QCD.

Findings

Three-loop anomalous dimension computed for the gluon mass operator.

Anomalous dimensions of localizing ghost fields derived at the same order.

QCD beta-function correctly recovered from ghost vertex renormalization.

Abstract

The three loop anomalous dimension for the gauge invariant, renormalizable, non-local mass operator for a gluon is computed in the MSbar scheme. In addition the anomalous dimensions of the associated localizing ghost fields are also deduced at the same order and it is shown that the three loop QCD beta-function correctly emerges from the gluon localizing ghost vertex renormalization.