Search for lepton flavour violation at LHCb

We report the first searches for lepton flavour violating $\tau$ decays at a hadron collider. In particular, a search for the decay $\tau \rightarrow \mu\mu\mu$ is presented, using data corresponding to an integrated luminosity of 1.0 fb$^{-1}$ collected at 7 TeV by LHCb in 2011. The upper limit on the branching ratio could be set, B($\tau^- \rightarrow \mu^+\mu^-\mu^-$) < 8.0 x 10$^{-8}$ at 90% confidence level (the inclusion of the charge conjugate process is included). In addition, we report on the search for heavy Majorana neutrinos in lepton number violating $B^- \rightarrow \pi^+\mu^-\mu^-$ decay (as well as in its charge conjugate). In this case, the whole LHCb dataset is used (1.0 fb$^{-1}$ at $\sqrt{s}$ = 7 TeV and 2 fb$^{-1}$ at $\sqrt{s}$ = 8 TeV). No signal is found, and a limit on the branching ratio is set, $B(B^- \rightarrow \pi^+\mu^-\mu^-$) < 4 x 10$^{-9}$ at 95% confidence level. This limit is then used to set limits on the coupling between the hypothetical Majorana neutrino and muons.