Lepton flavor violation by three units

The conservation of lepton flavor is a prediction of the Standard Model and is still an excellent approximate symmetry despite our observation of neutrino oscillations. Lepton flavor violation by one or two units have been discussed for decades, with several dedicated experiments exploring the vast model landscape but no discoveries so far. Here, we explore operators and processes that violate at least one lepton flavor by three units and identify testable signatures. In the Standard Model effective field theory, such operators already arise at mass dimension 7 and can be tested through their contributions to Michel parameters in leptonic decays. True neutrinoless charged-lepton flavor violation arises at mass dimension 10 and can realistically only be seen in the tau decay channels $\tau \to eee\bar{\mu}\bar{\mu}$ or $\tau \to \mu\mu\mu\bar{e}\bar{e}$, for example in Belle II. Testable rates for these tau decays require light new particles and subsequently predict an avalanche of remarkably clean but so-far unconstrained collider signatures.