Neutrino and \(Z'\) phenomenology in an anomaly-free \(\mathbf{U}(1)\) extension: role of higher-dimensional operators

Abstract

We consider an anomaly-free \(\mathrm{U}(1)\) extension of the Standard Model with three right-handed neutrinos (RHNs) and two complex scalars, wherein the charge assignments preclude all tree-level mass terms for the neutrinos. Considering this setup, in turn, to be only a low-energy effective theory, we introduce higher-dimensional terms {\em a la} Froggatt-Nielsen to naturally generate tiny neutrino masses. One of the RHNs turns out to be very light, thereby constituting the main decay mode for the \(Z'\) and hence relaxing the LHC dilepton resonance search constraints. This very RHN has a lifetime comparable to or bigger than the age of the Universe, and, hence, could account for a non-negligible fraction of the dark matter.