Sensitivity reach on heavy neutral leptons and $\tau$-neutrino mixing $|U_{\tau N}|^2 $ at the HL-LHC

The model of heavy neutral leptons (HNLs) is one of the well-motivated models beyond the standard model from both theoretical and phenomenological point of views. It is an indispensable ingredient to explain the puzzle of tiny neutrino masses and the origin of the matter-antimatter asymmetry in our Universe, based on the models in which the simplest type-I seesaw mechanism can be embedded. The HNL with a mass up to the electroweak scale is an attractive scenario which can be readily tested in present or near-future experiments including the LHC. In this work, we study the decay rates of HNLs and find the sensitive parameter space of the mixing angles between the active neutrinos and HNLs. Since there are fewer collider studies of the mixing between ντ and HNL in literature compared with those of νe and νμ for the HNL of mass in the electroweak scale, we focus on the channel pp→W±(*)+X→τ±N+X to search for HNLs at the LHC 14 TeV. The targeted signature consists of three prompt charged leptons, which include at least two tau leptons. After the signal-background analysis, we further set sensitivity bounds on the mixing |UτN|2 with MN at high-luminosity LHC (HL-LHC). We predict the testable bounds from HL-LHC can be stronger than the previous LEP constraints and electroweak precision data (EWPD), especially for MN≲50 GeV can reach down to |UτN|2≈5×10-6.