Higher order scheme-independent calculations of physical quantities in the conformal phase of a gauge theory

We consider an asymptotically free vectorial SU(N-c) gauge theory with N-f massless fermions in a representation R, having an infrared fixed point (IRFP) of the renormalization group at alpha(IR) in the conformal non-Abelian Coulomb phase. The cases with R equal to the fundamental, adjoint, and symmetric rank-2 tensor representation are considered. We present scheme-independent calculations of the anomalous dimension gamma(psi) over bar psi,IR to O(Delta(4)(f)) and beta'(IR) to O(Delta(5)(f)) at this IRFP, where.f is an N-f-dependent expansion parameter. Comparisons are made with conventional n-loop calculations and lattice measurements. As a test of the accuracy of the Delta(f) expansion, we calculate gamma(psi) over bar psi,IR to O(Delta(3)(f)) in N = 1 SU(N-c) supersymmetric quantum chromodynamics and find complete agreement, to this order, with the exactly known expression. The Delta(f) expansion also avoids a problem in which an IRFP may not be manifest as an IR zero of a higher n-loop beta function.