Freeze-in Dark Matter and $\Delta {\rm N}_{\rm eff}$ via Light Dirac Neutrino Portal

We propose a scenario where dark matter (DM) and dark radiation ($\Delta {\rm N}_{\rm eff}$) 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 and $\Delta {\rm N}_{\rm eff}$ via freeze-in mechanism to constrain the model parameters in the light of Planck 2018 data. We find that the scenario where $\phi$ remains out of equilibrium throughout or after a certain epoch allows more parameter space consistent with DM phenomenology and $\Delta {\rm N}_{\rm eff}$ in view of Planck 2018 data. The next generation experiments like CMB-S4, SPT-3G etc. will have the required sensitivities to probe a major portion of the entire model parameter space, offering a promising way of probing such non-thermal DM scenario which typical direct detection experiments are not much sensitive to.Comment: 38 pages, 7 captioned figure