$U(1)$-charged Dark Matter in three-Higgs-doublet models

TL;DR

This paper classifies all possible $U(1)$-based symmetries in three-Higgs-doublet models that can stabilize scalar Dark Matter, revealing new models and exploring their phenomenological implications across a broad mass range.

Contribution

It systematically categorizes $U(1)$ symmetry embeddings in 3HDMs and identifies previously unrecognized models with stable Dark Matter candidates.

Findings

Multiple $U(1)$-based Dark Matter models identified.

Numerical analysis shows viable Dark Matter candidates from 45 to 2000 GeV.

Many models preserve CP and feature degenerate Dark Matter pairs.

Abstract

We explore three-Higgs-doublet models that may accommodate scalar Dark Matter where the stability is based on an unbroken $U(1)$-based symmetry, rather than the familiar $\mathbb{Z}_2$ symmetry. Our aim is to classify all possible ways of embedding a $U(1)$ symmetry in a three-Higgs-doublet model. The different possibilities are presented and compared. All these models contain mass-degenerate pairs of Dark Matter candidates due to a $U(1)$ symmetry unbroken (conserved) by the vacuum. Most of these models preserve CP. In the CP-conserving case the pairs can be seen as one being even and the other being odd under CP or as having opposite charges under $U(1)$. Not all symmetries presented here were identified before in the literature, which points to the fact that there are still many open questions in three-Higgs-doublet models. We also perform a numerical exploration of the $U(1) \otimes U(1)$-symmetric 3HDM, this is the most general phase-invariant (real) three-Higgs-doublet model. The model contains a multi-component Dark Matter sector, with two independent mass scales. After imposing relevant experimental constraints we find that there are possible solutions throughout a broad Dark Matter mass range, 45-2000 GeV, the latter being a scan cutoff.