Displaced heavy neutrinos from $Z$ decays at the LHC

We study the LHC sensitivity to probe a long-lived heavy neutrino $N$ in the context of $Z$ models. We focus on displaced vertex signatures of $N$ when pair produced via a $Z$, decaying to leptons and jets inside the inner trackers of the LHC experiments. We explore the LHC reach with current long-lived particle search strategies for either one or two displaced vertices in association with hadronic tracks or jets. We focus on two well-motivated models, namely, the minimal $U(1)_{B-L}$ scenario and its $U(1)_{X}$ extension. We find that searches for at least one displaced vertex can cover a significant portion of the parameter space, with light-heavy neutrino mixings as low as $|V_{lN}|^2approx 10^{-17}$, and $l=e,mu$ accessible across GeV scale heavy neutrino masses.