New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories

TL;DR

This paper introduces new scheme transformations to analyze the scheme dependence of the infrared zero in the beta function of gauge theories, showing that the dependence is mild for moderate parameters.

Contribution

It presents two new one-parameter families of scheme transformations and applies them to study scheme dependence up to four-loop order in gauge theories.

Findings

Scheme dependence is mild for moderate transformation parameters.

New one-parameter scheme transformations are effective in analyzing beta function zeros.

Results quantify the scheme dependence in non-Abelian gauge theories.

Abstract

We present two new one-parameter families of scheme transformations and apply these to study the scheme dependence of the infrared zero in the beta function of an asymptotically free non-Abelian gauge theory up to four-loop order. Our results provide a further quantitative measure of this scheme dependence, showing that for moderate values of the gauge coupling and the parameter specifying the scheme transformation, this dependence is relatively mild. We also remark on a generalized multi-parameter family of rational scheme transformations.