Freeze-in Dark Matter via Light Dirac Neutrino Portal

We propose a scenario where dark matter (DM) can be generated non-thermally due to the presence of a light Dirac neutrino portal between the standard model (SM) and dark sector particles. The SM is minimally extended by three right handed neutrinos ($\nu_R$), a Dirac fermion DM candidate ($\psi$) and a complex scalar ($\phi$), transforming non-trivially under an unbroken $\mathbb{Z}_4$ symmetry while being singlets under the SM gauge group. While DM and $\nu_R$ couplings are considered to be tiny in order to be in the non-thermal or freeze-in regime, $\phi$ can be produced either thermally or non-thermally depending upon the strength of its Higgs portal coupling. We consider both these possibilities and find out the resulting DM abundance via freeze-in mechanism to constrain the model parameters in the light of Planck 2018 data. Since the interactions producing DM also produces relativistic $\nu_R$, we check the enhanced contribution to the effective relativistic degrees of freedom $\Delta {\rm N}_{\rm eff}$ in view of existing bounds as well as future sensitivities. We also check the stringent constraints on free-streaming length of such freeze-in DM from structure formation requirements. Such constraints can rule out DM mass all the way up to $\mathcal{O}(100 \, {\rm keV})$ keeping the $\Delta {\rm N}_{\rm eff} \leq \mathcal{O}(10^{-3})$, out of reach from near future experiments. Possible extensions of this minimal model can lead to observable $\Delta {\rm N}_{\rm eff}$ which can be probed at next generation experiments.