Coulomb gauge QCD from flow gauge at three loops

TL;DR

This paper investigates the cancellation of energy divergences in Coulomb gauge QCD at three loops, using an interpolating gauge to regularize divergences and analyzing the inclusion of UV divergent sub-graphs.

Contribution

It extends the analysis of energy divergence cancellation in Coulomb gauge QCD from two to three loops, introducing an interpolating gauge for regularization.

Findings

Sets of graphs free of energy divergences at three loops

Successful regularization of divergences using an interpolating gauge

Insights into radiative corrections to Christ-Lee terms

Abstract

We study the consistency of the non-Abelian Coulomb gauge. There are energy divergences in individual diagrams, which are known to cancel at 2-loop order when suitable sets of diagrams are summed. We investigate to 3-loop order the inclusion of UV divergent sub-graphs into the energy divergences. In all the examples we study, we find sets of graphs which are free of energy divergences. We make use of an interpolating gauge to regularise the energy divergences while integrals are manipulated. We comment on radiative corrections to the Christ-Lee terms in the Hamiltonian.