General Signals for Charged Lepton Flavor Violating Decays

We explore the most general phenomenology of charged lepton flavor violating (CLFV) decays of muon and tau leptons to the three body final states $(\bar{e}ee, \bar{\mu}\mu\mu, \bar{e}\mu\mu, \bar{\mu}\mu e,\bar{\mu}ee, \bar{e}e\mu)$. By constructing a complete basis of operators at each dimension, we derive the most general amplitudes for these decay processes. By considering constraints from unitarity and LEP, we show that operators of mass dimension 6 and 7 are the most likely to be observed in next generation experiments. Focusing on these dimensions, we compute the results of unpolarized (spin-averaged) decays parameterized in terms of the invariant masses of the daughter particles. We also compute the differential decay rates for polarized decays, in anticipation of the experimental search Mu3e, which expects to have a muon beam with $\sim 90\%$ polarization, and the Chiral Belle proposal, which aims to have a $70\%$ polarized electron beam. To determine the extent to which the operators may be distinguished experimentally, we plot the differential distributions for each operator, showing that they leave only a few possible degenerate explanations. Through a statistical analysis, we estimate the number of events needed to break the degeneracies using the angular information. These results are adapted to treat $\ell\to \ell' \nu \bar{\nu}$, where the angular distribution of the outgoing charged lepton has enhanced distinguishing power. With many Standard Model extensions predicting these CLFV decays, these results will better enable upcoming searches to identify and/or constrain physics beyond the Standard Model.