Search for lepton-flavor-violating ${\tau }^{-}\to {\mathrm{\ell }}^{-}\phi$ decays in 2019-2021 Belle II data

We report a search for lepton-flavor-violating decays ${\tau }^{-}\to {\mathrm{\ell }}^{-}\phi$ (${\mathrm{\ell }}^{-}=e^{-},{\mu }^{-}$) at the Belle II experiment, using a sample of electron-positron data produced at the SuperKEKB collider in 2019-2021 and corresponding to an integrated luminosity of 190 fb${}^{-1}$. We use a new untagged selection for $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ events, where the signal $\tau$ is searched for as a neutrinoless final state of a single charged lepton and a $\phi$ meson and the other $\tau$ is not reconstructed in any specific decay mode, in contrast to previous measurements by the BaBar and Belle experiments. We find no evidence for ${\tau }^{-}\to {\mathrm{\ell }}^{-}\phi$ decays and obtain upper limits on the branching fractions at 90% confidence level of 23 $\times {10}^{-8}$ and 9.7$\times {10}^{-8}$ for ${\tau }^{-}\to e^{-}\phi$ and ${\tau }^{-}\to {\mu }^{-}\phi$, respectively