Concept of a low energy electron-positron collider for dimuonium study

We discuss a low energy collider for production of the not yet discovered $\mu^+\mu^-$ bound state (dimuonium). In our design we follow the Brodsky-Lebed proposal of the large-crossing-angle $e^+e^-$ intersection, when the dimuonium carries non-zero momentum and decays to $e^+e^-$ pair far away from the beam collision region. The latter provides effective suppression of the Bhabha scattering background. We study experimental constraints and following requirements for the collider development. A preliminary layout is considered, the main parameters are obtained. The expected peak luminosity at the $\mu^+\mu^-$ production threshold is $8\times10^{31} cm^{-2}s^{-1}$. The same machine can be used for high statistic study of hadronic processes ($e^+e^-\to \pi^+\pi^-,\, \pi^+\pi^-\pi^0,\, \pi^0\gamma$ etc.) and search for rare processes in the center-of-mass energy range below 960 MeV.