$τ$ physics at LHCb

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

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