Possible Resonances in $\mu^+e^- \to \mu^- e^+$ Collisions

We study the possibility of discovering resonances in $\mu^+e^- \to \mu^- e^+$ and $e^-e^- \to \mu^- \mu^-$ collisions. We begin with the closely related problem of muonium--antimuonium transitions, where the experimental limit has just been improved by one order of magnitude. We show that the new limit enters a rather interesting mass and Yukawa coupling domain for neutral scalar bosons. The stringent $\mu\to e\gamma$ decay is evaded by invoking some multiplicative lepton number. Neutral and doubly charged scalar bosons give rise to distinguishable effects in muonium transitions. Alternatively, they could show up as spectacular resonance peaks in high energy $\mu^+e^- \to \mu^- e^+$and $e^-e^- \to \mu^- \mu^-$ collisions, respectively. This could occur independent of whether, but especially when, muonium-antimuonium transitions are experimentally observed.