Search for $B{}_s^0\to {\mathrm{\ell }}^{\mp }{\tau }^{\pm }$ with the Semi-leptonic Tagging Method at Belle

We present a search for the lepton-flavor-violating decays $B{}_s^0\to {\mathrm{\ell }}^{\mp }{\tau }^{\pm }$, where $\mathrm{\ell }=e,\mu$, using the full data sample of $121{\mathrm{f}\mathrm{b}}^{-1}$ collected at the $\mathrm{{\rm Y}}(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We use $B{}_s^0\bar{B}{}_s^0$ events in which one $B{}_s^0$ meson is reconstructed in a semileptonic decay mode and the other in the signal mode. We find no evidence for $B{}_s^0\to {\mathrm{\ell }}^{\mp }{\tau }^{\pm }$ decays and set upper limits on their branching fractions at $90\mathrm{\%}$ confidence level as $\mathcal{B}(B{}_s^0\to e^{\mp }{\tau }^{\pm })<14\times {10}^{-4}$ and $\mathcal{B}(B{}_s^0\to {\mu }^{\mp }{\tau }^{\pm })<7.3\times {10}^{-4}$. Our result represents the first upper limit on the $B{}_s^0\to e^{\mp }{\tau }^{\pm }$ decay rate.