| Summary: | A gauged U(1)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(1)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(1)X gauge boson (Z′) and its subsequent decay into a pair of RHNs. We first derive an updated upper limit on the new gauge coupling gX as a function of the Z′-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 (mlightest). We find that for mlightest≲10−5 eV, one of the RHNs in the minimal U(1)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.
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