# The $Z_3$ symmetric I(2+1)HDM

## TL;DR

This paper proposes a novel 3-Higgs Doublet Model with a $Z_3$ symmetry, introducing Hermaphrodite Dark Matter with two degenerate states, and demonstrates its consistency with current experimental constraints and relic density observations.

## Contribution

It introduces the I(2+1)HDM with $Z_3$ symmetry, featuring Hermaphrodite DM with two degenerate states, and analyzes its phenomenological viability.

## Key findings

- The model yields two mass-degenerate CP-opposite dark matter states.
- Relic density contributions of both states are equal and match observed values.
- The model is consistent with LHC Higgs measurements, EWPOs, and collider searches.

## Abstract

We introduce a 3-Higgs Doublet Model (3HDM) with two Inert (or dark) scalar doublets and an active Higgs one, hence termed I(2+1)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 parity, both of which contribute to DM dynamics, which we call \textit{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 Electro-Weak Precision Observables (EWPOs), Standard Model (SM)-like Higgs boson measurements at the Large Hadron Collider (LHC) and void searches for additional (pseudo)scalar states at the CERN machine and previous colliders.