Effective theory of light Dirac neutrino portal dark matter with observable ${ΔN_{\rm eff}}$

Abstract: We study the possibility of light Dirac neutrino portal dark matter (DM) in an effective field theory (EFT) 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 stabilised 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 thermalisation also ensures the thermalisation of $\nu_R$, leading to enhanced effective relativistic degrees of freedom $N_{\rm eff}$, 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 two UV completions based on the popularly studied gauges $\rm B-L$ and left-right symmetric model frameworks.