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This article presents the sensitivity of the ATLAS experiment to thelepton-flavour-violating decays of $\tau\to 3\mu$. A method utilising theproduction of $\tau$ leptons via $W\to\tau\nu$ decays is used. This method isapplied to the sample of 20.3 fb$^{-1}$ of $pp$ collision data at acentre-of-mass energy of 8 TeV collected by the ATLAS experiment at the LHC in2012. No event is observed passing the selection criteria, and the observed(expected) upper limit on the $\tau$ lepton branching fraction into threemuons, ${\rm Br}(\tau\to 3\mu)$, is $3.76\times 10^{-7}$ ($3.94\times 10^{-7}$)at 90% confidence level.

Probing lepton flavour violation via neutrinoless $\tau\longrightarrow 3\mu$ decays with the ATLAS detector