We consider an asymptotically free vectorial $\mathrm{SU}(N_c)$ gauge theory with $N_f$ massless fermions in a representation $R$, having an infrared fixed point (IRFP) of the renormalization group at ${\alpha }_{\mathrm{IR}}$ 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 ${\gamma }_{\overline{\psi }\psi ,\mathrm{IR}}$ to $O({\mathrm{\Delta }}_f^4)$ and ${\beta }_{\mathrm{IR}}^{\prime }$ to $O({\mathrm{\Delta }}_f^5)$ at this IRFP, where ${\mathrm{\Delta }}_f$ 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 ${\mathrm{\Delta }}_f$ expansion, we calculate ${\gamma }_{\overline{\psi }\psi ,\mathrm{IR}}$ to $O({\mathrm{\Delta }}_f^3)$ in $\mathcal{N}=1$ $\mathrm{SU}(N_c)$ supersymmetric quantum chromodynamics and find complete agreement, to this order, with the exactly known expression. The ${\mathrm{\Delta }}_f$ expansion also avoids a problem in which an IRFP may not be manifest as an IR zero of a higher $n$-loop beta function.

• Received 21 January 2017

DOI:https://doi.org/10.1103/PhysRevD.95.085012