Dark matter in a CP-violating three-Higgs-doublet model with $S_3$ symmetry

TL;DR

This paper investigates a specific three-Higgs-doublet model with $S_3$ symmetry that includes a dark matter candidate, explores its parameter space under constraints, and finds a viable dark matter mass range distinct from other models, also allowing spontaneous CP violation.

Contribution

It introduces and analyzes the C-III-a $S_3$-symmetric three-Higgs-doublet model with a dark matter candidate and spontaneous CP violation, providing a novel viable dark matter mass region.

Findings

Viable dark matter mass range: 6.5 to 44.5 GeV.

Distinct from Inert Doublet Model and other three-doublet models.

Model permits spontaneous CP violation.

Abstract

In spite of the success of the Standard Model of Particle Physics, there are some theoretical predictions which are not yet fully established experimentally as well as some experimental observations which cannot be fitted within its theoretical framework, thus requiring physics beyond the Standard Model. One of these is a hypothetical non-luminous form of matter - dark matter. Models with an extended scalar electroweak sector yield plausible dark matter candidates. In this paper we study a specific model, C-III-a, from a family of $S_3$-symmetric three-Higgs-doublet models. The model consists of two active SU(2) doublets and an inert one. The latter is inert due to a $\mathbb{Z}_2$ symmetry that survives the breaking of $S_3$, and would accommodate a dark matter particle. We explore the model numerically, based on theoretical and experimental constraints. After applying a number of successive checks over the parameter space we found a viable dark matter mass region in the range $[6.5;\,44.5]~\text{GeV}$. This region is drastically different from the Higgs-like dark matter states that have been proposed: the well-known Inert Doublet Model and models with three scalar doublets, with one or two inert doublets. Furthermore, the C-III-a model allows for spontaneous CP violation.