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

A search for $B_s^0\to {\tau }^{\pm }{\mu }^{\mp }$ 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 $B_s^0\to {\tau }^{\pm }{\mu }^{\mp }$ branching fraction of $$\mathcal{B}$\left( B^{0}{s}\to\tau^{\pm}\mu^{\mp}\right) < 4.2\times 10^{-5}$at$95%$confidencelevel\mathrm{.}Ifinsteadnocontributionfrom$B^{0}{s}\to\tau^{\pm}\mu^{\mp}$decaysisassumed,alimitof$$\mathcal{B}$\left( B^{0}\to\tau^{\pm}\mu^{\mp}\right) < 1.4\times 10^{-5}$ is obtained at $95\mathrm{\%}$ confidence level. These are the first limit on $\mathcal{B}(B_s^0\to {\tau }^{\pm }{\mu }^{\mp })$ and the world’s best limit on $\mathcal{B}(B^0\to {\tau }^{\pm }{\mu }^{\mp })$.