$Z_3$ symmetric inert ($2+1$)-Higgs-doublet model

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.

Figure 1

The combined relic density of the DM constituents $H_1$ and $A_1$ with respect to $m_{\mathrm{DM}}$ in benchmark scenario B for varying values of positive (left) and negative (right) $g_1$ coupling. The green band represents the DM observed relic density within $3\sigma$.

Figure 2

The combined relic density of the DM constituents $H_1$ and $A_1$ with respect to $m_{\mathrm{DM}}$ in benchmark scenario C for varying values of positive (left) and negative (right) $g_1$ coupling. The green band represents the DM observed relic density within $3\sigma$.

Figure 3

The combined relic density of the DM constituents $H_1$ and $A_1$ with respect to $m_{\mathrm{DM}}$ in benchmark scenario G for varying values of positive (left) and negative (right) $g_1$ coupling. The green band represents the DM observed relic density within $3\sigma$.

Figure 4

Regions where the model produces the DM relic density in $3\sigma$ agreement with Eq. (38) in the DM mass vs Higgs-DM coupling plane in green for scenario B for the input values in Table 2. The gray region represents areas where DM (co)annihilation is not strong enough and, as a result, DM is overproduced. The unshaded regions are where DM is underproduced.

Figure 5

Regions where the model produces the DM relic density in $3\sigma$ agreement with Eq. (38) in the DM mass vs Higgs-DM coupling plane in blue for scenario C for the input values in Table 2. The gray region represents areas where DM (co)annihilation is not strong enough and, as a result, DM is overproduced. The unshaded regions are where DM is underproduced.

Figure 6

Regions where the model produces the DM relic density in $3\sigma$ agreement with Eq. (38) in the DM mass vs Higgs-DM coupling plane in violet for scenario G for the input values in Table 2. The gray region represents areas where DM (co)annihilation is not strong enough and, as a result, DM is overproduced. The unshaded regions are where DM is underproduced.

Figure 7

Direct detection bounds on the points that saturate the relic density for scenarios B (top left), C (top right) and G (bottom). The solid red line corresponds to the current XENON1T limit above which any point is ruled out.

Figure 8

Indirect detection bounds on the points that saturate the relic density for scenarios B (top left), C (top right) and G (bottom). The solid red line corresponds to the current Fermi Large Area Telescope limit above which any point is ruled out.

Figure 9

The effect of the experimental constraints on the parameter space of benchmark scenarios B and C in the $m_{\mathrm{DM}}$, $g_1$ plane. The red-shaded regions are excluded by direct and indirect detection experiments while blue-shaded regions are excluded by the Higgs invisible branching ration bounds.