Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics

TL;DR

This paper develops a formalism to compute quark mass anomalous dimensions in QCD at O(1/N_f^2) using large N_f expansion, confirming known four-loop results and providing new six-loop coefficients.

Contribution

It introduces a method to calculate critical exponents in QCD at large N_f, connecting fixed points to a non-abelian Thirring model and extending perturbative results to higher loops.

Findings

Critical exponents match four-loop MSbar results.

New six-loop coefficients in renormalization group functions.

Explicit expression for eta in arbitrary covariant gauge.

Abstract

We present the formalism to calculate d-dimensional critical exponents in QCD in the large N_f expansion where N_f is the number of quark flavours. It relies in part on demonstrating that at the d-dimensional fixed point of QCD the critical theory is equivalent to a non-abelian version of the Thirring model. We describe the techniques used to compute critical two and three loop Feynman diagrams and as an application determine the quark wave function, eta, and mass renormalization critical exponents at O(1/N_f^2) in d-dimensions. Their values when expressed in relation to four dimensional perturbation theory are in exact agreement with the known four loop MSbar results. Moreover, new coefficients in these renormalization group functions are determined to six loops and O(1/N_f^2). The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for eta in arbitrary covariant gauge is given.