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

## TL;DR

This paper explores the production and detection of long-lived right-handed neutrinos at the LHC within a gauged U(1)_X model, highlighting potential signatures and constraints related to neutrino masses and collider searches.

## Contribution

It provides an updated collider analysis of U(1)_X models, deriving limits on gauge couplings, maximum RHN production rates, and conditions for long-lived neutrinos detectable via displaced vertices.

## Key findings

- Long-lived RHNs can exist for very light neutrino masses.
- LHC and MATHUSLA can detect displaced vertices from RHNs.
- Upper bounds on lightest neutrino mass can be inferred from RHN lifetime.

## Abstract

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 ($Z^\prime$) 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 $Z'$-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 ($m_{\rm lightest}$). 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 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.