Renormalization group equations and matching in a general quantum field theory with kinetic mixing

TL;DR

This paper develops simplified rules for applying two-loop renormalization group equations to general gauge theories with multiple Abelian factors, addressing complexities in effective theory matching.

Contribution

It extends existing RG equation frameworks to more complex gauge theories with multiple Abelian groups, including matching subtleties.

Findings

Provides simplified rules for two-loop RG equations in complex gauge theories

Addresses matching issues in effective gauge theory frameworks

Enhances the applicability of RG calculations to theories with multiple Abelian factors

Abstract

We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.