New method for non-standard invisible particle searches in tau lepton decays

Motivated by models proposed to explain the Standard Model anomalies, and the unprecedented $\tau^{+}\tau^{-}$ data to be collected by the Belle~II experiment during the next years, we study the kinematics of tau pair decays and propose a new method to search for lepton flavor violating processes in tau lepton decays to invisible beyond Standard Model particles, such as $\tau \to \ell \alpha$, where $\ell$ is either an electron or a muon, and $\alpha$ is a massive particle that escapes undetected. The new method improves by one order of magnitude the expected upper limit on the $\tau \to \ell \alpha$ production in 3x1 prong tau decays and establishes the possibility of performing this search in 1x1 prong tau decays which has not been previously considered.