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A search for the lepton flavour violating decay $\tau^-\to \mu^-\mu^+\mu^-$is performed with the LHCb experiment. The data sample corresponds to anintegrated luminosity of $1.0\mathrm{\,fb}^{-1}$ of proton-proton collisions ata centre-of-mass energy of $7\mathrm{\,Te\kern -0.1em V}$ and$2.0\mathrm{\,fb}^{-1}$ at $8\mathrm{\,Te\kern -0.1em V}$. No evidence is foundfor a signal, and a limit is set at $90\%$ confidence level on the branchingfraction, $\mathcal{B}(\tau^-\to \mu^-\mu^+\mu^-) < 4.6 \times 10^{-8}$.

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