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 -* W -* 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 ATLASinspired selection criteria, and optimize signal sensitivity. In particular, we demonstrate that appropriate cuts in the plane of dilepton 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 fb-1), existing bounds can be improved by more than an order of magnitude. Future high-luminosity runs may strengthen sensitivity by up to 3 orders of magnitude compared to current limits.