$\mu^+e^- <---> \mu^- e^+$ Transitions via Neutral Scalar Bosons

With $\mu\to e\gamma$ decay forbidden by multiplicative lepton number conservation, we study muonium--antimuonium transitions induced by neutral scalar bosons. Pseudoscalars do not induce conversion for triplet muonium, while for singlet muonium, pseudoscalar and scalar contributions add constructively. This is in contrast to the usual case of doubly charged scalar exchange, where the conversion rate is the same for both singlet and triplet muonium. Complementary to muonium conversion studies, high energy $\mu^+e^- \to \mu^- e^+$ and $e^-e^- \to \mu^- \mu^-$ collisions could reveal spectacular resonance peaks for the cases of neutral and doubly charged scalars, respectively.