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 ${\mathcal B}(\tau^-\to e^- \alpha) / {\mathcal B}(\tau^- \to e^- \bar\nu_e \nu_\tau)$ in the range $(1.1-9.7) \times 10^{-3}$ and on ${\mathcal B}(\tau^-\to \mu^- \alpha) / {\mathcal B}(\tau^- \to \mu^- \bar\nu_\mu \nu_\tau)$ 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.