Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

TL;DR

This paper develops a generalized class of momentum subtraction schemes for QCD, computes three-loop renormalization group functions in various gauges, and shows scheme independence of certain critical exponents within a specific conformal window.

Contribution

It introduces a parameterized family of renormalization schemes for QCD and calculates three-loop functions, extending previous MOM schemes and analyzing scheme dependence of critical exponents.

Findings

Three-loop renormalization group functions are established in new schemes.

Critical exponents at the Banks-Zaks fixed point are numerically scheme independent within a subrange.

The new schemes depend on a parameter $oldsymbol{}$ that generalizes existing MOM schemes.

Abstract

We introduce a more general set of kinematic renormalization schemes than the original momentum (MOM) subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter $\omega$ which tags the external momentum of one of the legs of the $3$-point vertex functions in Quantum Chromodynamics (QCD). In each of the three new schemes we renormalize QCD in the Landau and maximal abelian gauges and establish the three loop renormalization group functions in each gauge. As an application we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.