Search for lepton-flavor-violating ${\tau }^{-}\to {\mathrm{\ell }}^{-}{K}_s^0$ decays at Belle and Belle II

We present the results of a search for charged-lepton-flavor violating decays ${\tau }^{-}\to {\mathrm{\ell }}^{-}{K}_S^0$, where ${\mathrm{\ell }}^{-}$ is either an electron or a muon. We combine $e^{+}{e}^{-}$ data samples recorded by the Belle II experiment at the SuperKEKB collider (428 fb${}^{-1}$) with samples recorded by the Belle experiment at the KEKB collider (980 fb${}^{-1}$) to obtain a sample of 1.3 billion $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events. We observe 0 and 1 events and set $90\mathrm{\%}$ confidence level upper limits of $0.8\times {10}^{-8}$ and $1.2\times {10}^{-8}$ on the branching fractions of the decay modes ${\tau }^{-}\to e^{-}{K}_S^0$ and ${\tau }^{-}\to {\mu }^{-}{K}_S^0$, respectively. These are the most stringent upper limits to date.