Banks-Zaks fixed point analysis in momentum subtraction schemes

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.

33 latex pages, 25 tables, anc directory contains txt file with electronic version of renormalization group functions

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• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
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• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory