How about e μ Colliders for FCNC ? μ →

Inspired from the fact that new generation ee and μμ colliders are being seriously discussed, we propose a new type of particle collider – eμ collider! As our first attempt for exploring its physics potential, we demonstrate that the the eμ collision experiment can be much more efficient than present low-energy rare decay experiments and ee collision experiments in searching for lepton-number-violating Flavor Changing Neutral Current phenomena. [email protected] [email protected], [email protected] [email protected] 1 The progress of elementary particle physics has strongly depended on the advance of particle accelerator technology. It is most remarkable that the highest attainable center-of-mass energy has been rising almost exponentially since the 1930s. The rapid development of collider technology has contributed immensely to this success. Research on future particle accelerators and colliders has been progressing along two paths: (i) one is exploring the energy (and luminosity) frontiers so that we could probe very high energy (and very rare) phenomena, and (ii) the other is developing a totally new accelerator technology. A typical example of the second case is a μμ collider which has been drawing considerable attention of many physicists [1] in the world, regarding the search for Higgs particle(s); since the mass of μ is about 200 times the mass of e, Higgs particles can be produced at the μμ collider about 40000 times more frequently than at the ee collider for √ s = m H . In this letter, we propose a new type of particle collider. It is an eμ collider! In connection with the problem of muonium-antimuonium transitions [2], μe ↔ μe, through doubly charged Higgs, ∆, dilepton gauge boson, X, or flavor changing neutral scalar bosons, H and A, the process μe → μe has been first illustrated at a talk given by Hou [3]. As a definite example of its physics potential, we demonstrate that the eμ collision experiment can be much more efficient compared to present lowenergy rare decay experiments and ee collision experiments, such as μ → eγ, μ → eee and ee → eμ, in searching for lepton-number-violating Flavor Changing Neutral Current (FCNC) phenomena, which must be the strongest evidence for new physics beyond the Standard Model (SM). In the SM, the probability of μ → eγ and μ → eee are absolutely zero, while their experimental upper limits are 4.9 × 10 [6] and 1.0 × 10 [7], respectively. The ee and pp̄ colliders which have been most powerful tools in the high-energy particle physics experiments, or even a μμ § Tree-level FCNC has been theoretically considered by using new models, such as the generalized two Higgs doublet model [4], as well as in various collider and decay processes [5].