Sterile Neutrino Portal Dark Matter with $Z_3$ Symmetry

In this paper, we consider the sterile neutrino portal dark matter with $Z_3$ symmetry. This model further extends the canonical type-I seesaw with a fermion singlet $\chi$ and a scalar singlet $\phi$. Under the $Z_3$ symmetry, the dark sector transforms as $\chi\to e^{i2\pi/3}\chi, \phi\to e^{i2\pi/3}\phi$, while the standard model particles and the sterile neutrino $N$ transform trivially. Besides the interactions as $y_{N} \phi \bar{\chi}N$ and $\lambda_{H\phi} (H^\dag H) (\phi^\dag \phi)$ allowed in the $Z_2$ symmetry, the $Z_3$ symmetry also introduces two new terms, i.e., $y_\chi \phi \overline{\chi^{c}} \chi$ and $\mu\phi^3/2$. These new interactions induce additional semi-annihilation processes as $\chi\chi\to N\chi$ and $\phi\phi\to h\phi$ for WIMP dark matter. We then perform a comprehensive analysis of the phenomenology of this $Z_3$ symmetric model. Viable parameter space is explored under the constraints from dark matter relic density, Higgs invisible decay, indirect and direct detection for both fermion and scalar dark matter. We find that the semi-annihilation channels $\chi\chi\to N\chi$ and $\phi\phi\to N\chi$ can lead to quite different phenomena from the $Z_2$ symmetric model, which provides a viable pathway to distinguish these two kinds of model.