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

We search for lepton-flavor-violating $τ^-\to e^-α$ and $τ^-\toμ^-α$ decays, where $α$ 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 $τ^-\to e^-\barν_e ν_τ$ and $τ^-\to μ^-\barν_μν_τ$ decays. We report 95\% confidence-level upper limits on the branching-fraction ratio ${\mathcal B}(τ^-\to e^- α) / {\mathcal B}(τ^- \to e^- \barν_e ν_τ)$ in the range $(1.1-9.7) \times 10^{-3}$ and on ${\mathcal B}(τ^-\to μ^- α) / {\mathcal B}(τ^- \to μ^- \barν_μν_τ)$ in the range $(0.7-12.2) \times 10^{-3}$ for $α$ masses between 0 and 1.6 GeV/c$^2$. These results provide the most stringent bounds on invisible boson production from $τ$ decays.