## Long-lived TeV-scale right-handed neutrino production at the LHC in gauged U(1)(X) model

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A gauged (U{\left(1\right)}*{X}) extension of the Standard Model is a simple and consistent framework to naturally incorporate three right-handed neutrinos (RHNs) for generating the observed light neutrino masses and mixing by the type-I seesaw mechanism. We examine the collider testability of the (U{\left(1\right)}*{X}) model, both in its minimal form with the conventional charges, as well as with an alternative charge assignment, via the resonant production of the (U{\left(1\right)}*{X}) gauge boson (({Z}^{\prime })) and its subsequent decay into a pair of RHNs. We first derive an updated upper limit on the new gauge coupling ({g}*{X}) as a function of the ({Z}^{\prime })-boson mass from the latest LHC dilepton searches. Then we identify the maximum possible cross section for the RHN pair-production under these constraints. Finally, we investigate the possibility of having one of the RHNs long-lived, even for a TeV-scale mass. Employing the general parametrization for the light neutrino mass matrix to reproduce the observed neutrino oscillation data, we perform a parameter scan and find a simple formula for the maximum RHN lifetime as a function of the lightest neutrino mass eigenvalue (({m}*{\mathrm{lightest}})). We find that for ({m}*{\mathrm{lightest}}\lesssim {10}^{-5}) eV, one of the RHNs in the minimal (U{\left(1\right)}_{X}) scenario can be long-lived with a displaced-vertex signature which can be searched for at the LHC and/or with a dedicated long-lived particle detector, such as MATHUSLA. In other words, once a long-lived RHN is observed, we can set an upper bound on the lightest neutrino mass in this model.