Four loop renormalization of QCD in the Curci-Ferrari gauge
Abstract
We renormalize Quantum Chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MSbar) scheme. We reproduce the four loop QCD MSbar beta-function from the Slavnov-Taylor identity for this gauge which relates the coupling constant renormalization to the gluon, Faddeev-Popov ghost and gauge parameter anomalous dimensions. This is carried out for a nonzero gauge parameter, without having to evaluate a vertex function. The anomalous dimension of the BRST invariant dimension two gluon and ghost mass term is deduced from a similar Slavnov-Taylor identity for this gauge. Consequently we construct the renormalization group functions in the minimal momentum subtraction scheme to four loops. As a corollary we deduce the five loop beta-function and quark mass anomalous dimensions in the same scheme. We also outline the pros and cons of employing the Curci-Ferrari gauge to access the six loop QCD beta-function in the MSbar scheme.
Cite
@article{arxiv.2412.20950,
title = {Four loop renormalization of QCD in the Curci-Ferrari gauge},
author = {J. A. Gracey},
journal= {arXiv preprint arXiv:2412.20950},
year = {2025}
}
Comments
35 latex pages, 3 figures, anc directory contains electronic version of renormalization group functions and conversion functions in the Curci-Ferrari gauge; minor corrections and references added