Sterile Neutrino Portal Dark Matter from Semi-Production

In this paper, we study the feeble sterile neutrino portal dark matter under the $Z_3$ symmetry. The dark sector consists of one fermion singlet $\chi$ and one scalar singlet $\chi$, which transforms as $\chi \to e^{i2\pi \mathrm{/}3}\chi ,\phi \to e^{i2\pi \mathrm{/}3}\phi$ under the $Z_3$ symmetry. Regarding fermion singlet $\chi$ as the dark matter candidate, the new interaction terms $y_{\chi }\phi \overline{{\chi }^c}\chi$ and $\mu {\phi }^3\mathrm{/}2$ could induce various new production channels. For instance, when $m_{\phi }>2m_{\chi }$, the pair decay $\phi \to \chi \chi$ could be the dominant channel, rather than the delayed decay $\phi \to \chi \nu$. Another appealing scenario is when the dark sector is initially produced through the scattering process as $NN\to \chi \chi ,NN\to \phi \phi ,h\nu \to \chi \phi$, then the semi-production processes $N\chi \to \phi \phi ,N\phi \to \phi \chi ,N\chi \to \chi \chi$ could lead to the exponential growth of dark sector abundances. The phenomenology of sterile neutrino and the cosmological impact of the dark scalar are also considered in the $Z_3$ symmetric model.