Minimal Dirac Neutrino Mass Models from $U(1)_R$ Gauge Symmetry and Left-Right Asymmetry at Colliders

In this work, we propose minimal realizations for generating Dirac neutrino masses in the context of a right-handed abelian gauge extension of the Standard Model. Utilizing only $U(1)_R$ symmetry, we address and analyze the possibilities of Dirac neutrino mass generation via (a) \textit{tree-level seesaw} and (b) \textit{radiative correction at the one-loop level}. One of the presented radiative models implements the attractive \textit{scotogenic} model that links neutrino mass with Dark Matter (DM), where the stability of the DM is guaranteed from a residual discrete symmetry emerging from $U(1)_R$. Since only the right-handed fermions carry non-zero charges under the $U(1)_R$, this framework leads to sizable and distinctive Left-Right asymmetry as well as Forward-Backward asymmetry discriminating from $U(1)_{B-L}$ models and can be tested at the colliders. We analyze the current experimental bounds and present the discovery reach limits for the new heavy gauge boson $Z^{\prime}$ at the LHC and ILC. Furthermore, we also study the associated charged lepton flavor violating processes, dark matter phenomenology and cosmological constraints of these models.