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

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 ℤ₂ 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) × 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.