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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 conformalnon-Abelian Coulomb phase. The cases with $R$ equal to the fundamental,adjoint, and symmetric rank-2 tensor representation are considered. We presentscheme-independent calculations of the anomalous dimension$\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^4)$ and $\beta'_{IR}$ to$O(\Delta_f^5)$ at this IRFP, where $\Delta_f$ is an $N_f$-dependent expansionparameter. Comparisons are made with conventional $n$-loop calculations andlattice measurements. As a test of the accuracy of the $\Delta_f$ expansion, wecalculate $\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^3)$ in ${\cal N}=1$SU($N_c$) supersymmetric quantum chromodynamics and find complete agreement, tothis order, with the exactly known expression. The $\Delta_f$ expansion alsoavoids a problem in which an IRFP may not be manifest as an IR zero of a higher$n$-loop beta function.

Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory