Abstract
We introduce a three-Higgs doublet model (3HDM) with two inert (or dark) scalar doublets and an active Higgs one, hence termed $\mathrm{I}(2+1)\mathrm{HDM}$, in the presence of a discrete ${Z}_{3}$ symmetry acting upon the three doublet fields. We show that such a construct yields a dark matter (DM) sector with two mass-degenerate states of opposite $CP$ quantum number, both of which contribute to DM dynamics, which we call ``hermaphrodite DM,'' distinguishable from a (single) complex DM candidate. We show that the relic density contributions of both states are equal, saturating the observed relic density compliant with (in)direct searches for DM as well as other experimental data impinging on both the dark and Higgs sectors of the model, chiefly, in the form of electroweak precision observables, Standard Model-like Higgs boson measurements at the Large Hadron Collider and void searches for additional (pseudo)scalar states at the CERN machine and previous colliders.
Highlights
The discovery of a Higgs boson by the Large Hadron Collider (LHC) in July 2012 [1,2] has confirmed that electroweak symmetry breaking (EWSB) is triggered by the Higgs mechanism
If one assumes that doublet representations of Higgs fields are those chosen by nature to implement EWSB, which is entirely plausible in the light of the fact that only such a structure is able to give mass to the WÆ and Z bosons of the Standard Model (SM) while preserving a massless photon, thereby in turn enabling unification of electromagnetic (EM) and weak interactions, one may wonder what can models with a generic number N of Higgs doublets, in turn defining the class of N-Higgs doublet models (NHDMs), produce in terms of new physics signals
Motivated by two problems in the SM, from the experimental side, the absence of viable dark matter (DM) candidates, and, from the theoretical side, the lack of an explanation for the three families of matter, we have postulated a 3HDM, wherein two doublets are inert, and one is active. This so-called Ið2 þ 1ÞHDM version of the 3HDM has been repeatedly studied in the literature and shown to be viable against both theoretical constraints and experimental limits when a Z2 symmetry is imposed by hand onto the Lagrangian, according to which all SM fields, including the active doublet generating the Z, WÆ and Higgs masses measured by experiment, are even while all those emerging from the two inert doublets are odd
Summary
The discovery of a Higgs boson by the Large Hadron Collider (LHC) in July 2012 [1,2] has confirmed that electroweak symmetry breaking (EWSB) is triggered by the Higgs mechanism. In this paper, we will probe Z3 symmetric Ið2 þ 1ÞHDM solutions that satisfy several constraints for the low DM mass region which are instead excluded in the Z3 symmetric Ið1þ1ÞHDM plus singlet This Z3 symmetric Ið2 þ 1ÞHDM is the model we will be concerned with, building upon the one introduced and studied in Refs. In an NHDM, the generic scalar potential symmetric under a group G of phase rotations can be written as the sum of two parts: 3A 3HDM with ð0; v; v0Þ vacuum alignment has been considered in [10] wherein it was termed IDM2. Using our nomenclature, this model may be referred to as the Ið1 þ 2ÞHDM.
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