Constraining Heavy Neutral Leptons Coupled to the Tau-Neutrino Flavor at the Large Hadron Collider

Displaced vertex (DV) signatures at colliders offer a powerful probe of new long-lived particles beyond the Standard Model. Among the best-motivated candidates are heavy neutral leptons (HNLs) - heavier counterparts of Standard Model neutrinos - which can account for the origin of neutrino masses and potentially produce di-leptonic DV signatures. In this study, we demonstrate how existing DV searches at the LHC can be extended to probe HNLs that couple predominantly to the tau-neutrino flavor. While current search strategies rely on identifying a prompt lepton alongside a displaced vertex, we show that analyzing events without a prompt lepton enables sensitivity to the process $pp \to W \to \tau N$, where the tau decays hadronically and the HNL subsequently decays to a lepton pair and a neutrino. We perform detailed Monte Carlo simulations of this process with HNLs decaying to $\mu^+\mu^-$ or $e^+e^-$ final states, apply ATLAS-inspired selection criteria, and optimize signal sensitivity. In particular, we demonstrate that appropriate cuts in the plane of di-lepton invariant mass and DV radial position significantly enhance signal visibility. We propose several such optimized strategies and show that even with Run 2 data $139~\text{fb}^{-1}$ , existing bounds can be improved by more than an order of magnitude. Future high-luminosity runs may strengthen sensitivity by up to three orders of magnitude compared to current limits.