Search for lepton flavor-violating decay modes $B^0\to K_S^0τ^\pm\ell^\mp~(\ell=μ, e)$ with hadronic $B$-tagging at Belle and Belle II
We present the first search for the lepton flavor-violating decay modes $B^0 \rightarrow K_S^0 τ^\pm \ell^\mp~(\ell=μ, e)$ 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 $B^0 \rightarrow K_S^0 τ^\pm \ell^\mp$ decays and set 90\% confidence level upper limits on the branching fractions in the range of $[0.8,\,3.6]\times10^{-5}$.