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The model of heavy neutral leptons (HNLs) is one of the well-motivated modelsbeyond the standard model (BSM) from both theoretical and phenomenologicalpoint of views. It is an indispensable ingredient to explain the puzzle of tinyneutrino masses and the origin of the matter-antimatter asymmetry in ourUniverse, based on the models in which the simplest Type-I seesaw mechanism canbe embedded. The HNL with a mass up to the electroweak scale is an attractivescenario which can be readily tested in present or near-future experimentsincluding the LHC. In this work, we study the decay rates of HNLs and find thesensitive parameter space of the mixing angles between the active neutrinos andHNLs. Since the mixing between $ \nu_{\tau} $ and HNL is not well establishedin literature compared with those of $\nu_e$ and $\nu_{\mu}$ for the HNL ofmass in the electroweak scale, we focus on the channel $ pp\rightarrowW^{\pm(\ast)} + X\rightarrow \tau^{\pm} N + X$ to search for HNLs at the LHC 14TeV. The targeted signature consists of three prompt charged leptons, whichinclude at least two tau leptons. After the signal-background analysis, wefurther set sensitivity bounds on the mixing $ |U_{\tau N}|^2 $ with $ M_N $ atHigh-Luminosity LHC (HL-LHC). We predict the testable bounds from HL-LHC can bestronger than the previous LEP constraints and Electroweak Precision Data(EWPD), especially for $ M_N \lesssim $ 50 GeV can reach down to $ |U_{\tauN}|^2 \approx 2\times 10^{-6} $.

Sensitivity Reach on the Heavy Neutral Leptons and $\tau$-Neutrino Mixing $|U_{\tau N}|^2 $ at the HL-LHC