Effective theory of light Dirac neutrino portal dark matter with observable $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$

We study the possibility of light Dirac neutrino portal dark matter (DM) in an effective field theory setup. Dirac nature of light neutrino automatically includes its right chiral part ${\nu }_R$ which, in our setup, also acts like a portal between DM and the standard model (SM) particles. Considering a Dirac fermion singlet DM stabilized by an unbroken $Z_2$ symmetry, we write down all possible dimension-6 effective operators involving DM-${\nu }_R$ as well as ${\nu }_R$-SM which conserve $Z_2$, global lepton number and SM gauge symmetries. DM thermalization also ensures the thermalization of ${\nu }_R$, leading to enhanced effective relativistic degrees of freedom $N_{\mathrm{e}\mathrm{f}\mathrm{f}}$, within reach of future cosmic microwave background (CMB) experiments. We study the complementarity among DM and CMB related observations for different Lorentz structures of effective operators. We also propose a UV complete gauged $\mathrm{B}-\mathrm{L}$ symmetric model with Dirac neutrino portal dark matter.