One loop renormalization of the non-local gauge invariant operator min_U (A^U_mu)^2 in QCD

TL;DR

This paper calculates the one-loop anomalous dimension of a gauge-invariant non-local operator in QCD, demonstrating gauge parameter independence and linking it to a local operator in Landau gauge.

Contribution

It provides the first explicit one-loop anomalous dimension calculation for the gauge-invariant non-local operator min_U (A^U_mu)^2 in arbitrary covariant gauges.

Findings

Gauge parameter cancels out in the anomalous dimension.

Result matches the local operator (A^a_mu)^2 in Landau gauge.

Method exploits Zwanziger's expansion of the operator.

Abstract

We compute the one loop anomalous dimension of the gauge invariant dimension two operator min_U (A^U_mu)^2, where U is an element of the gauge group, by exploiting Zwanziger's expansion of the operator in terms of gauge invariant non-local n leg operators. The computation is performed in an arbitrary linear covariant gauge and the cancellation of the gauge parameter in the final anomalous dimension is demonstrated explicitly. The result is equivalent to the one loop anomalous dimension of the local dimension two operator (A^a_mu)^2 in the Landau gauge.