Geometric Minimization of Softly-Broken Potentials

TL;DR

This paper extends the geometric minimization method to analyze softly-broken multi-Higgs potentials with symmetries, providing a new approach to find and classify minima in these models.

Contribution

It introduces a generalized geometric minimization technique that accounts for soft symmetry breaking in multi-Higgs models, enabling analytic solutions.

Findings

Successfully applied to an S4 multi-Higgs model

Classified the minima of the softly-broken potential

Provided a systematic approach for similar models

Abstract

We study the minimization of multi-Higgs models with symmetries that are softly-broken. The powerful method of geometric minimization enables analytic minimization of multi-Higgs models with large symmetries. When these symmetries are softly-broken, the method needs to be adapted. We propose a useful generalization that considers the effect of the soft-breaking terms to the quadratic part of the potential, by applying the procedure to restricted orbit spaces. We exemplify our novel methodology by finding and classifying the minima for an $S_4$ multi-Higgs model that is softly-broken with specific terms.