Search for lepton flavor-violating decay modes $B^0\to K_S^0{\tau }^{\pm }{\mathrm{\ell }}^{\mp }(\mathrm{\ell }=\mu ,e)$ with hadronic $B$-tagging at Belle and Belle II

We present the first search for the lepton flavor-violating decay modes $B^0\to K_S^0{\tau }^{\pm }{\mathrm{\ell }}^{\mp }(\mathrm{\ell }=\mu ,e)$ using the 711 fb${}^{-1}$ and 365 fb${}^{-1}$ data samples recorded by the Belle and Belle II detectors, respectively. We use a hadronic $B$-tagging technique, and search for the signal decay in the system recoiling against the fully reconstructed $B$ meson. We find no evidence for $B^0\to K_S^0{\tau }^{\pm }{\mathrm{\ell }}^{\mp }$ decays and set 90% confidence level upper limits on the branching fractions in the range of $[0.8,3.6]\times {10}^{-5}$.