Lepton flavor violating decay of true muonium: $\boldsymbol{(\mu^+ \mu^-) \to \mu^\pm e^\mp}$

Abstract

We propose a new channel for probing charged lepton flavor violation (CLFV): the decay of true muonium into a lepton pair of different flavor, $(\mu^+ \mu^-) \to \mu^\pm e^\mp$. This purely leptonic two-body decay provides a clean experimental signature in the form of energetic, oppositely charged leptons. It is sensitive not only to photonic dipole interactions but also to four-fermion contact interactions, and is free from hadronic uncertainties in theoretical predictions. We evaluate the branching ratios induced by scalar-, vector-, and dipole-type CLFV operators. Our results show that the branching ratio can reach up to $\mathcal{O}(10^{-20})$ within current experimental bounds. This decay mode may be discovered as an early-stage physics opportunity of the muon collider program by utilizing the large number of muons produced at its front end.