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

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.

103 pages, 5 figures, v2: added references, minor text changes

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• Systematic analysis of 3HDM symmetries
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• Assessing boundedness from below in the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-symmetric three-Higgs-doublet model: algorithm and machine learning
• The Hilbert Series and the Flavor Invariants of the 3HDM