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We present a search for the lepton-flavor-violating decays $B{}^0_s\rightarrow \ell^{\mp}\tau^{\pm}$, where $\ell = e, \mu$, using the full datasample of $121~\mathrm{fb}^{-1}$ collected at the $\Upsilon(5S)$ resonance withthe Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We use$B{}^0_s \overline{B}{}^0_s$ events in which one $B{}^0_s$ meson isreconstructed in a semileptonic decay mode and the other in the signal mode. Wefind no evidence for $B{}^0_s \rightarrow \ell^{\mp}\tau^{\pm}$ decays and setupper limits on their branching fractions at $90\%$ confidence level as$\mathcal{B}(B{}^0_s \rightarrow e^{\mp}\tau^{\pm}) < 14 \times 10^{-4}$ and$\mathcal{B}(B{}^0_s \rightarrow \mu^{\mp}\tau^{\pm}) < 7.3 \times 10^{-4}$.Our result represents the first upper limit on the $B{}^0_s \rightarrowe^{\mp}\tau^{\pm}$ decay rate.

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