Searches of lepton-flavour-violating decays of the Higgs bosons with the ATLAS detector at the HL-LHC

This note presents a study for the prospect of the searches for lepton-flavour-violating decays of the Higgs bosons with $3000\,\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s} = 14$TeV using the ATLAS detector at the HL-LHC. The expected HL-LHC results are estimated by the extrapolation of the Run 2 dataset, accounting for, among others, the increase in the integrated luminosity and potential reduction of uncertainties associated with particle reconstruction with the upgraded ATLAS detector. This work presents the searches for $H\rightarrow e\tau$ and $H\rightarrow\mu\tau$ as independent signals. Two independent approaches of the background estimation are employed.