Search for the lepton flavour violating and baryon number violating decays $\tau^- \rightarrow \bar{p} \mu^+ \mu^-$ and $\tau^- \rightarrow p \mu^- \mu^-$

A search is made for the lepton flavour violating and baryon number violating decays $\tau^- \rightarrow \bar{p} \mu^+\mu^-$ and $\tau^- \rightarrow p \mu^- \mu^-$ using data, corresponding to an integrated luminosity of $1.0$ fb$^{-1}$, 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 $D^-$ mesons. In the analysis of the data, the $\tau^-$ production rate is normalised to the control channel $D_s \rightarrow \phi(\mu^+ \mu^-)\pi^-$. The observed numbers of events are consistent with the background expectations, and upper limits $\mathcal{B}(\tau^- \rightarrow \bar{p} \mu^+ \mu^-) < 4.5 (3.4) \times 10^{-7}$ and $\mathcal{B}(\tau^- \rightarrow p \mu^- \mu^-) < 6.0 (4.6) \times 10^{-7}$ are set at 95 % (90 %) confidence level.