Scheme and gauge dependence of QCD fixed points at five loops

TL;DR

This study investigates the dependence of QCD fixed points on schemes and gauges at five-loop order, revealing multiple stable fixed points and improved convergence of critical exponents across different methods.

Contribution

It demonstrates the scheme and gauge dependence of QCD fixed points at high loop order, including the existence of multiple stable fixed points and their consistency across various gauges and schemes.

Findings

Multiple infrared stable fixed points identified in different gauges.

Fixed point solutions vary between schemes, with some persisting below MSbar scheme thresholds.

Critical exponents show improved convergence at higher loop orders.

Abstract

We analyse 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 MSbar 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.