New physics in multi-lepton tau decays

Dark particles with lepton-flavor-violating couplings to the tau lepton can induce rare neutrinoless $\tau$ decays with large final state multiplicities. We study models where transitions of the type $\tau^\pm\to \ell^\pm\,\phi$, with $\phi$ a light new particle, initiate a chain of decays in the dark sector that terminate with decays into electrons, muons, or pions. These decay cascades appear as rare five or even seven-body $\tau$ decays with multiple reconstructable resonances. We survey several representative models: kinetically mixed dark photon, gauged $L_i-L_j$ models, and other more exotic charge assignments such as chiral $U(1)'$ extensions of the Standard Model. The main new ingredient is the possibility of flavor violation at very high scales. In these models, a number of channels that have not yet been searched for experimentally, such as $\tau\to 5\mu$, $\tau\to 3\mu\,2e$, $\tau\to \mu\,4e$, and hadronic channels like $\tau\to \mu\,4\pi$, typically dominate over the previously-considered signatures such as $\tau \to 3\mu$. While some of the models, such as the gauged $L_i-L_j$ ones, also contain more challenging channels with missing energy due to decays to neutrinos, they can still be searched for via fully visible channels.