Search for Lepton-Flavor-Violating <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>τ</mml:mi></mml:math> Decays to a Lepton and an Invisible Boson at Belle II

We search for lepton-flavor-violating τ^{-}→e^{-}α and τ^{-}→μ^{-}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^{-}→e^{-}ν[over ¯]_{e}ν_{τ} and τ^{-}→μ^{-}ν[over ¯]_{μ}ν_{τ} decays. We report 95% confidence-level upper limits on the branching-fraction ratio B(τ^{-}→e^{-}α)/B(τ^{-}→e^{-}ν[over ¯]_{e}ν_{τ}) in the range (1.1-9.7)×10^{-3} and on B(τ^{-}→μ^{-}α)/B(τ^{-}→μ^{-}ν[over ¯]_{μ}ν_{τ}) in the range (0.7-12.2)×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.