On the impact of kinetic mixing in beta functions at two-loop

TL;DR

This paper investigates how kinetic mixing affects the two-loop renormalization group equations in models with multiple U(1) gauge groups, revealing significant impacts on parameter evolution and potential stability.

Contribution

It provides a comprehensive numerical analysis of kinetic mixing effects on two-loop beta functions using PyR@TE 2 for the SM B-L model.

Findings

Kinetic mixing significantly alters the evolution of parameters.

Proper accounting of kinetic mixing is crucial for accurate RGEs.

Kinetic mixing can change conclusions about scalar potential stability.

Abstract

Kinetic mixing is a fundamental property of models with a gauge symmetry involving several $\mathrm{U}(1)$ group factors. In this paper, we perform a numerical study of the impact of kinetic mixing on beta functions at two-loop. To do so, we use the recently published PyR@TE 2 software to derive the complete set of RGEs of the SM B-L model at two-loop including kinetic mixing. We show that it is important to properly account for kinetic mixing as the evolution of the parameters with the energy scale can change drastically. In some cases, these modifications can even lead to a different conclusion regarding the stability of the scalar potential.