Search for the lepton-flavor-violating ${\tau }^{-}\to e^{\mp }{\mathrm{\ell }}^{\pm }{\mathrm{\ell }}^{\mp }$ decays at Belle II

We present the result of a search for the charged-lepton-flavor violating decays ${\tau }^{-}\to e^{\mp }{\mathrm{\ell }}^{\pm }{\mathrm{\ell }}^{-}$, where $\mathrm{\ell }$ is a muon or an electron, using a data sample with an integrated luminosity of 428 fb${}^{-1}$ recorded by the Belle II experiment at the SuperKEKB $e^{+}{e}^{-}$ collider. The selection of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events containing a signal candidate is based on an inclusive-tagging reconstruction and on a boosted decision tree to suppress background. Upper limits on the branching fractions between 1.3 and 2.5 $\times {10}^{-8}$ are set at the 90% confidence level. These results are the most stringent bounds to date for four of the modes.