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

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.

arXiv commentVersion accepted in PRD; 6 pages

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• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking
• RG-stable parameter relations of a scalar field theory in absence of a symmetry
• Weyl Consistency Conditions from a local Wilsonian Cutoff
• ARGES -- Advanced Renormalisation Group Equation Simplifier
• Gradient Flow and Holography from a Local Wilsonian Cutoff
• General Gauge-Yukawa-Quartic $\beta$-Functions at 4-3-2--Loop Order