Revisiting two dark matter candidates in $S_3$-symmetric three-Higgs-doublet models

TL;DR

This paper investigates two dark matter candidates within $S_3$-symmetric three-Higgs-doublet models, analyzing their properties, viable mass ranges, and compatibility with experimental data, including LHC and indirect detection constraints.

Contribution

It introduces two specific $S_3$-symmetric three-Higgs-doublet implementations with dark matter candidates, refining their parameter space considering recent experimental constraints.

Findings

Viable dark matter mass ranges identified: 52.5-89 GeV and 6.5-44.5 GeV.

Models do not support heavy dark matter candidates around 500 GeV.

CP violation affects the structure and properties of the dark matter candidates.

Abstract

Models with an extended scalar electroweak sector are well motivated. Such models could accommodate a dark matter candidate if there is an additional scalar representation with a vanishing vacuum expectation value and, in addition, there are no couplings between fermions and the dark matter candidate. The most natural way to have these conditions implemented is to consider models where an underlying symmetry is imposed. Governed by this, we consider a three-Higgs-doublet model with an $S_3$ symmetry. Within this framework there are different implementations which could possibly accommodate a dark matter candidate. The family of $S_3$-symmetric three-Higgs-doublet implementations arises due to different vacua and, as a result, different minimisation conditions. In this framework the dark matter candidate falls into the class of weakly interacting massive particles. The dark matter candidate is associated with an $\mathbb{Z}_2$ symmetry which survives spontaneous symmetry breaking and is a remnant of the $S_3$ symmetry. We explore two cases, they share many aspects of the Type-I two-Higgs-doublet model plus an inert SU(2) doublet. The main difference between these two cases is the presence of an irremovable phase, which leads to CP violation in one of the implementations. The two candidate cases differ from other previously studied models with three scalar doublets by the fact that they do not allow for heavy dark matter candidates, $\mathcal{O}(500)\text{ GeV}$. Valid dark matter regions were identified as $m_\mathrm{DM} \in [52.5,\,89]~\text{GeV}$ for a model without CP violation and $m_\mathrm{DM} \in [6.5,\,44.5]~\text{GeV}$ for a model with CP violation. In the present work we refine the parameter space by applying additional checks to our previous work coming from LHC data and from indirect detection data.