Search for Lepton-Flavor-Violating $\tau$ Decays to a Lepton and an Invisible Boson at Belle II

We search for lepton-flavor-violating ${\tau }^{-}\to e^{-}\alpha$ and ${\tau }^{-}\to {\mu }^{-}\alpha$ decays, where $\alpha$ is an invisible spin-0 boson. The search uses electron-positron collisions at $10.58$ GeV center-of-mass energy with an integrated luminosity of $62.8$ fb${}^{-1}$, produced by the SuperKEKB collider and collected with the Belle II detector. We search for an excess in the lepton-energy spectrum of the known ${\tau }^{-}\to e^{-}{\bar{\nu }}_e{\nu }_{\tau }$ and ${\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau }$ decays. We report 95% confidence-level upper limits on the branching-fraction ratio $\mathcal{B}({\tau }^{-}\to e^{-}\alpha )\mathrm{/}\mathcal{B}({\tau }^{-}\to e^{-}{\bar{\nu }}_e{\nu }_{\tau })$ in the range $(1.1-9.7)\times {10}^{-3}$ and on $\mathcal{B}({\tau }^{-}\to {\mu }^{-}\alpha )\mathrm{/}\mathcal{B}({\tau }^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }{\nu }_{\tau })$ in the range $(0.7-12.2)\times {10}^{-3}$ for $\alpha$ masses between 0 and 1.6 GeV/c${}^2$. These results provide the most stringent bounds on invisible boson production from $\tau$ decays.