Scheme Transformations in the Vicinity of an Infrared Fixed Point

TL;DR

This paper investigates how scheme transformations near an infrared fixed point affect the analysis of gauge theories, showing reduced freedom compared to ultraviolet fixed points and assessing scheme dependence of the fixed point and anomalous dimensions.

Contribution

It constructs a specific scheme transformation to evaluate scheme dependence of infrared fixed points in SU(N) gauge theories with fermions.

Findings

Less scheme transformation freedom near IR fixed points

Constructed transformation from $ar{MS}$ to a scheme with zero three-loop term

Assessed scheme dependence of IR fixed points and anomalous dimensions

Abstract

We analyze the effect of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions. We show that there is far less freedom in carrying out such scheme transformations in this case than at an ultraviolet fixed point. We construct a transformation from the $\bar{MS}$ scheme to a scheme with a vanishing three-loop term in the $\beta$ function and use this to assess the scheme dependence of an infrared fixed point in SU($N$) theories with fermions. Implications for the anomalous dimension of the fermion bilinear operator are also discussed.