General RGEs for dimensionful couplings in the $\overline{\mathrm{MS}}$ scheme

TL;DR

This paper derives the renormalization group equations for dimensionful couplings in gauge theories within the $ar{MS}$ scheme using the dummy field method, completing the set of RGEs for such theories.

Contribution

It introduces a method to derive RGEs for dimensionful couplings in the $ar{MS}$ scheme, extending previous work focused on dimensionless parameters.

Findings

Derived RGEs for dimensionful couplings using the dummy field method.

Implemented the complete set of RGEs in the PyR@TE software.

Facilitates automatic computation of RGEs for general gauge theories.

Abstract

Recently, Poole & Thomsen have presented the Renormalization Group Equations (RGEs) in the $\overline{\mathrm{MS}}$ scheme for dimensionless parameters of a general renormalizable gauge theory in a new formalism based on the Local Renormalization Group. In this Letter, we apply the dummy field method to the expressions in this formalism in order to derive the RGEs for the dimensionful couplings which so far have been missing in this approach. The complete set of RGEs has been implemented in a new version of the public code PyR@TE (arXiv:2007.12700) dedicated to the automatic computation of the RGEs for any general renormalizable (non-supersymmetric) gauge theory.