Phenomenology of the gauge symmetry for right-handed fermions

In this paper we investigate the phenomenology of the U(1) gauge symmetry for right-handed fermions, where three right-handed neutrinos are introduced for anomalies cancellation. Constraints on the new gauge boson $Z_{\mathbf{R}}$ arising from $Z-Z^\prime$ mixing as well as the upper bound of $Z^\prime$ production cross section in di-lepton channel at the LHC are presented. We further study the neutrino mass generation and the phenomenology of $Z_{\mathbf{R}}$-portal dark matter in this model. The lightest right-handed neutrino can be the cold dark matter candidate stabilized by a $Z_2$ flavor symmetry. Our results show that active neutrino masses can be generated via the modified type-II seesaw mechanism; right-handed neutrino dark matter is available only for its mass at near the resonant regime of the SM Higgs and/or the new bosons; constraint from the dilepton search at the LHC is stronger than that from the $Z-Z^\prime$ mixing only for $g_\mathbf{R}<0.121$, where $g_\mathbf{R}$ is the new gauge coupling.