Search for the lepton flavour violating decay $\tau^-\to \mu^+\mu^-\mu^-$

A search is made for the lepton flavour violating decay $\tau^-\to \mu^+\mu^-\mu^-$ using $1.0$~fb$^{-1}$ of data collected at $\sqrt{s}=7$ TeV by LHCb in 2011. In LHCb, $\tau^{-}$ leptons are copiously produced, almost exclusively from decays of $B$, $D_s^-$ and $D^0$ mesons. In the analysis of the data, the $\tau^{-}$ production rate is normalised to the control channel $D_s^-\to \phi (\mu^+\mu^-) \pi^-$. The observed number of events is consistent with the background expectation, and an upper limit ${\cal B}(\tau^-\to \mu^+\mu^-\mu^-) < 7.8 (6.3) \times 10^{-8}$ is set at 95 % (90 %) confidence level.