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

Abstract

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 ${\gamma }_{\bar{\psi }\psi ,IR}$ to $O({\Delta }_f^4)$ and ${\beta }_{IR}^{\prime }$ to $O({\Delta }_f^5)$ at this IRFP, where ${\Delta }_f$ 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 ${\Delta }_f$ expansion, we calculate ${\gamma }_{\bar{\psi }\psi ,IR}$ to $O({\Delta }_f^3)$ in $\mathcal{N}=1$ 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.

Comments: 6 pages, latex, 3 figures