Renormalizability of the local composite operator A^2 in linear covariant gauges

TL;DR

This paper proves that the local composite operator A^2 in Yang-Mills theories with linear covariant gauges is multiplicatively renormalizable to all orders and calculates its anomalous dimension at two loops.

Contribution

It demonstrates the all-order multiplicative renormalizability of A^2 and provides a two-loop anomalous dimension calculation in the MSbar scheme.

Findings

A^2 is multiplicatively renormalizable to all orders.

The two-loop anomalous dimension of A^2 is computed.

The analysis is performed within algebraic renormalization in linear covariant gauges.

Abstract

The local composite operator $A_{\mu}^{2}$ is analysed within the algebraic renormalization in Yang-Mills theories in linear covariant gauges. We establish that it is multiplicatively renormalizable to all orders of perturbation theory. Its anomalous dimension is computed to two-loops in the MSbar scheme.