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

Abstract

We present the results of a search for charged-lepton-flavor violating decays $\ddot{I}{„}^{-}\to {\ell }^{-}{K}_S^0$, where ${\ell }^{-}$ 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 $e^{+}{e}^{-}\to \ddot{I}{„}^{+}\ddot{I}{„}^{-}$ events. We observe 0 and 1 events and set $90\%$ confidence level upper limits of $0.8\times 10^{-8}$ and $1.2\times 10^{-8}$ on the branching fractions of the decay modes $\ddot{I}{„}^{-}\to e^{-}{K}_S^0$ and $\ddot{I}{„}^{-}\to \hat{I}{¼}^{-}{K}_S^0$, respectively. These are the most stringent upper limits to date.