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

We consider an asymptotically free vectorial SU(Nc) gauge theory with Nf massless fermions in a representation R, having an infrared fixed point (IRFP) of the renormalization group at αIR 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 γψψ,IR to O(Δf4) and βIR′ to O(Δf5) at this IRFP, where Δf is an Nf-dependent expansion parameter. Comparisons are made with conventional n-loop calculations and lattice measurements. As a test of the accuracy of the Δf expansion, we calculate γψψ,IR to O(Δf3) in N=1 SU(Nc) supersymmetric quantum chromodynamics and find complete agreement, to this order, with the exactly known expression. The Δf expansion also avoids a problem in which an IRFP may not be manifest as an IR zero of a higher n-loop beta function.