Radiative Dirac Neutrino Mass with Dark Matter and it's implication to $0ν4β$ in the $U(1)_{B-L}$ extension of the Standard Model
The Standard Model gauge symmetry is extended by $U(1)_{B-L}$ which when spontaneously broken leads to residual $\mathbb{Z}_4$ symmetry. $U(1)_{B-L}$ gauge symmetry made anomaly free by introducing exotic SM singlets with corresponding $U(1)_{B-L}$ charges of $13$, $-14$, and $15$. $\mathbb{Z}_4$ symmetry ensures the Dirac nature of neutrinos, simultaneously stabilizing dark matter. Dirac neutrino mass is generated through scotogenic scenario. Dark matter, direct detection, cosmological constraints, and collider constraints analysis is performed. $\mathbb{Z}_4$ symmetry predicts the exact absence of neutrinoless double beta decay ($0ν2β$) and gives a prediction for an enhanced neutrinoless quadruple beta decay ($0ν4β$) via which this model can be tested. Model allows for Majorana dark matter as well as for long-lived dark matter candidates.