Renormalization of vacuum expectation values in spontaneously broken gauge theories

TL;DR

This paper calculates the one-loop and two-loop beta-functions for vacuum expectation values in gauge theories, revealing how VEVs renormalize differently from scalar fields and applying this to supersymmetric models.

Contribution

It introduces a novel interpretation of VEV renormalization as an anomalous dimension, extending the understanding of beta-functions in gauge theories, including supersymmetric models.

Findings

VEVs have distinct renormalization behavior from scalar fields in R_xi gauge.

The anomalous dimension interpretation simplifies understanding VEV renormalization.

Explicit beta-functions for VEVs and tan(beta) are provided for MSSM, NMSSM, and E6SSM.

Abstract

We compute one-loop and two-loop beta-functions for vacuum expectation values (VEVs) in gauge theories. In R_xi gauge the VEVs renormalize differently from the respective scalar fields. We focus particularly on the origin and behavior of this difference and show that it can be interpreted as the anomalous dimension of a certain scalar background field, leading to simple direct computation and qualitative understanding. The results are given for generic as well as supersymmetric gauge theories. These complement the set of well-known gamma- and beta-functions of Machacek/Vaughn. As an application, we compute the beta-functions for VEVs and tan(beta) in the MSSM, NMSSM and E6SSM.