Computation of quark mass anomalous dimension at O(1/N-f(2)) in quantum chromodynamics

We present the formalism to calculate d-dimensional critical exponents in Q CD 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 Q CD the critical theory is equivalent to a non-abelian version of the Thirri ng model. We describe the techniques used to compute critical two- and thre e-loop Feynman diagrams and as an application determine the quark wave func tion, eta, and mass renormalization critical exponents at O(1/N-f(2)) in d dimensions. Their values when expressed in relation to four-dimensional per turbation theory are in exact agreement with the known four-loop <(MS)over bar> results. Moreover, new coefficients in these renormalization group fun ctions 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 expressio n for eta in arbitrary covariant gauge is given. (C) 2000 Elsevier Science B.V. All rights reserved.