$Z^\prime$ Portal Dark Matter with Observable $ΔN_{\rm eff}$

In the conventional $Z^\prime$ portal dark matter scenario, the prediction of detectable dark matter $\chi$ typically relies on the collider sensitivities of $Z^\prime$ and direct detection, where the Majorana type right-handed neutrinos are usually assumed. However, if the right-handed neutrinos $\nu_R$ are Dirac type, they will contribute to the additional effective number of relativistic species $\Delta N_{\rm eff}$, which brings different detectable predictions for $Z^\prime$ portal dark matter. In light of the great improvement of $\Delta N_{\rm eff}$ for the upcoming experiments, we investigate the $Z^\prime$ portal dark matter with Dirac type $\nu_R$. Under the $U(1)_{B-L}$ symmetry, this model includes $\nu_R$ with $U(1)_{B-L}$ charge $Q_{\nu_R}=-1$ and $\chi$ with arbitrary $Q_\chi$ beyond the SM. Based on the relation in the production of $\chi$ and $\nu_R$, both the WIMP and FIMP dark matter through the $Z^\prime$ portal scenario are considered. We perform a comprehensive exploration of the viable parameter space under the constraints from $\Delta N_{\rm eff}$ induced by thermal and non-thermal $\nu_R$, perturbative limit, dark matter direct and indirect detection, and collider searches of $Z^\prime$.