Four loop renormalization of QCD in the Curci-Ferrari gauge


Gracey, JA ORCID: 0000-0002-9101-2853 (2025) Four loop renormalization of QCD in the Curci-Ferrari gauge Physical Review D, 111 (6). 065016-. ISSN 2470-0010, 2470-0029

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Abstract

We renormalize quantum chromodynamics (QCD) when gauge fixed in the nonlinear Curci-Ferrari gauge to four loops in the modified minimal subtraction (MS¯) scheme. We reproduce the four loop QCD MS¯ β-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 β-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 β-function in the MS¯ scheme.

Item Type: Article
Uncontrolled Keywords: 5106 Nuclear and Plasma Physics, 5107 Particle and High Energy Physics, 4902 Mathematical Physics, 49 Mathematical Sciences, 51 Physical Sciences
Divisions: Faculty of Science & Engineering
Faculty of Science & Engineering > School of Physical Sciences
Depositing User: Symplectic Admin
Date Deposited: 24 Apr 2025 08:12
Last Modified: 24 Jan 2026 05:11
DOI: 10.1103/PhysRevD.111.065016
Open Access URL: https://doi.org/10.1103/PhysRevD.111.065016
Related Websites:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3191530
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