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) tree-level seesaw and (b) radiative correction at the one-loop level. One of the presented radiative models implements the attractive 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′ 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.