Renormalization in an interpolating gauge in Yang-Mills theory

TL;DR

This paper investigates the renormalization properties of an interpolating gauge in Yang-Mills theory, connecting Feynman and Coulomb gauges, and reveals novel features such as field mixing and counter-term structures.

Contribution

It provides a comprehensive analysis of the renormalization of the theta-gauge, including the renormalization of the interpolation parameter and new counter-term structures at two loops.

Findings

Renormalization of the theta parameter in the interpolating gauge.

Field mixing and scaling behaviors observed.

New counter-term structures identified at two-loop order.

Abstract

The Coulomb gauge in QCD is the only explicitly unitary gauge. But it suffers from energy-divergences which means that it is not rigorously well-defined. One way to define it unambiguously is as the limit of a gauge interpolating between the Feynman gauge and the Coulomb gauge. This interpolating gauge is characterized by a parameter theta and the Coulomb gauge is obtained in the limit theta tends to 0. We study the renormalization of this theta-gauge for all values of theta. Novel features include field mixing as well as scaling, the renormalization of the theta parameter itself, and the appearance of new counter-term structures at two-loop order.