Spontaneous symmetry breaking in the $S_3$-symmetric scalar sector

TL;DR

This paper thoroughly analyzes the vacua of an $S_3$-symmetric three-Higgs-doublet potential, exploring spontaneous symmetry breaking, CP violation, and stability constraints within different mathematical frameworks.

Contribution

It provides a comprehensive analysis of the vacua in $S_3$-symmetric three-Higgs-doublet models, including mappings between frameworks and implications for dark matter.

Findings

Identification of parameter regions with specific vacua

Analysis of spontaneous CP violation scenarios

Constraints on vacuum stability and residual symmetries

Abstract

We present a detailed study of the vacua of the $S_3$-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.