Three loop anomalous dimension of non-singlet quark currents in the RI′ scheme

Abstract

We renormalize QCD at three loops in the modified regularization invariant, RI′, scheme in arbitrary covariant gauge and deduce that the four loop β-function is equivalent to the MS result. The anomalous dimensions of the scalar, vector and tensor currents are then determined in the RI′ scheme at three loops by considering the insertion of the operator in a quark two-point function. The expression for the scalar current agrees with the quark mass anomalous dimension and we deduce an expression for the four loop RI′ mass anomalous dimension in arbitrary covariant gauge and for any Lie group.