Search for lepton-flavor-violating tau decays to $\mathrm{\ell }\alpha$ at Belle

We report a search for the lepton-flavor-violating decays ${\tau }^{\pm }\to {\mathrm{\ell }}^{\pm }\alpha$~($\mathrm{\ell }=e,\mu$), where $\alpha$ is an undetected spin-0 particle, such as an axion-like particle using $736\times {10}^6$ tau lepton pairs collected by the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We find no evidence of signal and obtain the most stringent upper limits on the branching fractions at 95% confidence level: $\mathcal{B}({\tau }^{\pm }\to e^{\pm }\alpha )$ $<$ $(0.4$–$6.4)\times {10}^{-4}$ and $\mathcal{B}({\tau }^{\pm }\to {\mu }^{\pm }\alpha )$ $<$ $(0.2$–$3.5)\times {10}^{-4}$ at 95% confidence level for an $\alpha$ mass in the range $0.0\le m_{\alpha }\le 1.6$~GeV/$c^2$.