Scheme and gauge dependence of QCD fixed points at five loops

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 CurciFerrari 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.

Automated summary

We analyze the fixed points of QCD at high loop order in different renormalization schemes and gauges. We find that the Banks-Zaks fixed point solutions persist in the minimal momentum subtraction scheme for lower values of Nf than in the MS scheme in the canonical linear covariant gauge. By considering the parameter of the linear covariant gauge as a second coupling constant, we confirm the existence of a second Banks-Zaks twin critical point that is infrared stable, up to five loops. We also observe a similar infrared stable fixed point in the CurciFerrari and maximal Abelian gauges, which persists in different schemes including kinematic ones. We show that the critical exponent estimates improve in convergence and agreement across various schemes with increased loop order.