Prospects for lepton flavour violation measurements in $\tau\rightarrow 3\mu$ decays with the ATLAS detector at the HL-LHC

This note estimates the ATLAS detector sensitivity to measure the branching fraction of the lepton flavour violating decay $\tau\rightarrow 3\mu$ with 3000 fb$^{-1}$ of 14 TeV proton-proton collision data expected during the HL-LHC campaign. Two sources of $\tau$ leptons are considered: W-bosons and heavy flavour hadrons. The estimation is a projection of the measurement of the search for $\tau\rightarrow 3\mu$ decays in $W\to\tau\nu$ events performed by the ATLAS experiment with data collected in 2012. Several scenarios and expected upper limits at different acceptance and background rejection levels are discussed.