Search for the lepton-flavour-violating decays $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ and $B^{0}\to\tau^{\pm}\mu^{\mp}$

A search for $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ and $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays is performed using data corresponding to an integrated luminosity of 3 fb$^{-1}$ of proton-proton collisions, recorded with the LHCb detector in 2011 and 2012. For this search, the $\tau$ lepton is reconstructed in the $\tau^{-}\to\pi^{-}\pi^{+}\pi^{-}\nu_{\tau}$ channel. No significant signal is observed. Assuming no contribution from $B^{0}\to\tau^{\pm}\mu^{\mp}$ decays, an upper limit is set on the $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ branching fraction of $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right)<4.2\times 10^{-5}$ at $95\%$ confidence level. If instead no contribution from $B^{0}_{s}\to\tau^{\pm}\mu^{\mp}$ decays is assumed, a limit of $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right)<1.4\times 10^{-5}$ is obtained at $95\%$ confidence level. These are the first limit on $\mathcal{B}\left( B^{0}_{s}\to\tau^{\pm}\mu^{\mp}\right)$ and the world's best limit on $\mathcal{B}\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right)$.