Low scale Dirac leptogenesis and dark matter with observable $$\Delta N_{\mathrm{eff}}$$ Δ N eff

We propose a gauged $$B-L$$ extension of the standard model (SM) where light neutrinos are of Dirac type by virtue of tiny Yukawa couplings. To achieve leptogenesis, we include additional heavy Majorana fermions without introducing any $$B-L$$ violation by two units. An additional scalar doublet with appropriate $$B-L$$ charge can allow such heavy fermion coupling with SM leptons so that out-of-equilibrium decay of the former can lead to generation of lepton asymmetry. Due to the $$B-L$$ gauge interactions of the decaying fermion, the criteria of successful Dirac leptogenesis can also constrain the gauge sector couplings. The same $$B-L$$ gauge sector parameter space can also be constrained from dark matter requirements if the latter is assumed to consist of SM singlet particles with non-zero $$B-L$$ charges, which also keep the model anomaly free. The same $$B-L$$ gauge interactions also lead to additional thermalised relativistic degrees of freedom $$\Delta N_{\mathrm{eff}}$$ from light Dirac neutrinos which are tightly constrained by Planck 2018 data. While there exists parameter space from the criteria of successful leptogenesis, dark matter and $$\Delta N_{\mathrm{eff}}$$ even after incorporating the latest collider bounds, the currently allowed parameter space can be probed by future measurements of $$\Delta N_{\mathrm{eff}}$$ .