The search for $\tau\to\mu\mu\mu$ at LHCb

The charged lepton flavour violating decay $\tau\to\mu\mu\mu$ is searched for, using the LHCb experiment. Violation of lepton flavour in the charged lepton sector is unobserved to date. Within the Standard Model of particle physics including neutrino oscillation, the branching fraction is expected to be umeasureable small and an observation would be an unambiguous sign for physics beyond the Standard Model. Over $10^{11}$ $\tau$ leptons have been produced in proton-proton collisions at LHCb during the first run of the LHC. Most of them in decays of $D_s$ mesons. Compared to previous experiments at electron-positron colliders, the signature of $\tau\to\mu\mu\mu$ is harder to identify in hadronic collisions and background processes are more abundant. A multivariate event classification has been developed to distinguish a possible signal from background events. The number of $\tau$ leptons produced in the LHCb acceptance is estimated by measuring the yield of $D_s\to\phi(\mu\mu)\pi$ decays. The sensitivity reached by analysing LHCb data corresponding to 3 fb$^{-1}$ is sufficient to constrain the branching fraction of $\tau\to\mu\mu\mu$ to be smaller than $7.1\times10^{-8}$ at $90\,\%$ confidence level.