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Scheme and gauge dependence of QCD fixed points at five loops

J. A. Gracey1, R. H. Mason1, Thomas A. Ryttov2, and R. M. Simms1

  • 1Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, P.O. Box 147, Liverpool, L69 3BX, United Kingdom
  • 2CP3-Origins, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark

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Phys. Rev. D 108, 045006 – Published 11 August, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.045006

Abstract

We analyze the fixed points of QCD at high loop order in a variety of renormalization schemes and gauges across the conformal window. We observe that in the minimal momentum subtraction scheme solutions for the Banks-Zaks fixed point persist for values of Nf below that of the MS¯ scheme in the canonical linear covariant gauge. By treating the parameter of the linear covariant gauge as a second coupling constant we confirm the existence of a second Banks-Zaks twin critical point, which is infrared stable, to five loops. Moreover a similar and parallel infrared stable fixed point is present in the Curci-Ferrari and maximal Abelian gauges which persists in different schemes including kinematic ones. We verify that with the increased available loop order, critical exponent estimates show an improvement in convergence and agreement in the various schemes.

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Phys. Rev. D 108, 045006– Published 11 August, 2023
  • Received 30 June 2023
  • Accepted 12 July 2023
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