Computation of quark mass anomalous dimension at O(1/N2) in quantum chromodynamics

We present the formalism to calculate d -dimensional critical exponents in QCD in the large Nf expansion where Nf 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, η , and mass renormalization critical exponents at O(1/Nf2) in d dimensions. Their values when expressed in relation to four-dimensional perturbation theory are in exact agreement with the known four-loop MS results. Moreover, new coefficients in these renormalization group functions are determined to six-loops and O(1/Nf2) . The computation of the exponents in the Schwinger Dyson approach is also provided and an expression for η in arbitrary covariant gauge is given.