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A gauged $U(1)_X$ extension of the Standard Model is a simple and consistentframework to naturally incorporate three right-handed neutrinos (RHNs) forgenerating the observed light neutrino masses and mixing by the type-I seesawmechanism. We examine the collider testability of the $U(1)_X$ model, both inits minimal form with the conventional charges, as well as with an alternativecharge assignment, via the resonant production of the $U(1)_X$ gauge boson($Z^\prime$) and its subsequent decay into a pair of RHNs. We first derive anupdated upper limit on the new gauge coupling $g_X$ as a function of the$Z'$-boson mass from the latest LHC dilepton searches. Then we identify themaximum possible cross section for the RHN pair-production under theseconstraints. Finally, we investigate the possibility of having one of the RHNslong-lived, even for a TeV-scale mass. Employing the general parametrizationfor the light neutrino mass matrix to reproduce the observed neutrinooscillation data, we perform a parameter scan and find a simple formula for themaximum RHN lifetime as a function of the lightest neutrino mass eigenvalue($m_{\rm lightest}$). We find that for $m_{\rm lightest}\lesssim 10^{-5}$ eV,one of the RHNs in the minimal $U(1)_X$ scenario can be long-lived with adisplaced-vertex signature which can be searched for at the LHC and/or with adedicated long-lived particle detector, such as MATHUSLA. In other words, oncea long-lived RHN is observed, we can set an upper bound on the lightestneutrino mass in this model.

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