Banks-Zaks fixed point analysis in momentum subtraction schemes

TL;DR

This paper investigates the properties of the Banks-Zaks fixed point in QCD across different schemes, providing estimates of critical exponents that are largely scheme independent for certain quark flavor ranges.

Contribution

It offers a detailed analysis of the quark mass anomalous dimension and beta-function at the Banks-Zaks fixed point in various MOM schemes, including five-loop estimates in the MSbar scheme.

Findings

Exponents are scheme independent for specific quark flavor ranges.

Estimated the quark mass anomalous dimension exponent as 0.263-0.268 for SU(3) with 12 flavors.

Provided scheme-independent estimates of critical exponents at the Banks-Zaks fixed point.

Abstract

We analyse the critical exponents relating to the quark mass anomalous dimension and beta-function at the Banks-Zaks fixed point in Quantum Chromodynamics (QCD) in a variety of representations for the quark in the momentum subtraction (MOM) schemes of Celmaster and Gonsalves. For a specific range of values of the number of quark flavours, estimates of the exponents appear to be scheme independent. Using the recent five loop modified minimal subtraction (MSbar) scheme quark mass anomalous dimension and estimates of the fixed point location we estimate the associated exponent as 0.263-0.268 for the SU(3) colour group and 12 flavours when the quarks are in the fundamental representation.