Singlet-doublet fermion dark matter with Dirac neutrino mass, $(g-2{)}_{\mu }$ and $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$

We study the possibility of generating light Dirac neutrino mass via scotogenic mechanism where singlet-doublet fermion dark matter (DM) plays non-trivial role in generating one-loop neutrino mass, anomalous magnetic moment of muon $(g-2{)}_{\mu }$ as well as additional relativistic degrees of freedom $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ within reach of cosmic microwave background (CMB) experiments. We show that the Dirac nature of neutrinos can bring interesting correlations within the parameter space satisfying the ${(g-2)}_{\mu }$ anomaly and DM relic density and the effective relativistic degrees of freedom $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$. While we stick to thermal singlet doublet DM with promising detection prospects, both thermal and non-thermal origin of $\mathrm{\Delta }{N}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ have been explored. In addition to detection prospects at DM, $(g-2)$ and other particle physics experiments, the model remains verifiable at future CMB experiments like CMB-S4, SPT-3G.