Three loop MSbar renormalization of the Curci-Ferrari model and the dimension two BRST invariant composite operator in QCD

TL;DR

This paper performs a three-loop MSbar renormalization of the Curci-Ferrari model and a related BRST invariant operator in QCD, providing detailed anomalous dimensions relevant for gauge theories.

Contribution

It presents the first three-loop renormalization of the Curci-Ferrari model and the associated BRST invariant operator in an arbitrary covariant gauge.

Findings

Renormalization constants computed at three loops in MSbar scheme.

Anomalous dimensions of the dimension two operator in QCD and QED derived.

Results applicable to understanding mass operators in gauge theories.

Abstract

The massless Curci-Ferrari model with N_f flavours of quarks is renormalized to three loops in the MSbar scheme in an arbitrary covariant gauge with parameter alpha. The renormalization of the BRST invariant dimension two composite operator, 1/2 (A^a_\mu)^2 - alpha \bar{c}^a c^a, which corresponds to the mass operator in the massive Curci-Ferrari model, is determined by renormalizing the Green's function where the operator is inserted in a ghost two-point function. Consequently the anomalous dimension of the QCD Landau gauge operator, 1/2 (A^a_\mu)^2, and the (gauge independent) photon mass anomalous dimension in QED are both deduced at three loops.