$\tau$ physics at LHCb

We report on the first searches for lepton flavour violating ${\tau }^{-}$ decays at a hadron collider. These include searches for the lepton flavour violating decay ${\tau }^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{-}$ and the lepton flavour and baryon number violating decays ${\tau }^{-}\to \bar{p}{\mu }^{+}{\mu }^{-}$ and ${\tau }^{-}\to p{\mu }^{-}{\mu }^{-}$. Upper limits of $\mathcal{B}({\tau }^{-}\to {\mu }^{+}{\mu }^{-}{\mu }^{-})<4.6\times {10}^{-8}$, $\mathcal{B}({\tau }^{-}\to \bar{p}{\mu }^{+}{\mu }^{-})<3.4\times {10}^{-7}$ and ${\cal B}(\tau^-\to p\mu^-\mu^-) < 4.6 \times 10^{-7}$ are set at 90% confidence level. A measurement of the inclusive $Z\to {\tau }^{+}{\tau }^{-}$ cross-section at 7 TeV is also reported and is found to be consistent with the Standard Model. The ratio of the $Z\to {\tau }^{+}{\tau }^{-}$ cross-section to the $Z\to {\mu }^{+}{\mu }^{-}$ cross-section is found to be consistent with lepton universality.