The bound mu+ mu- system

We consider the hyperfine structure, the atomic spectrum and the decay channels of the bound mu+ mu- system (dimuonium). The annihilation lifetimes of low-lying atomic states of the system lie in the nanosecond range range. The decay rates could be measured by detection of the decay products (high energy photons or electron-positron pairs). The hyperfine structure splitting of the dimuonic system and its decay rate are influenced by electronic vacuum polarization effects in the far time-like asymptotic region. This constitutes a previously unexplored kinematic regime. We evaluate next--to-leading order radiative corrections to the decay rate of low-lying atomic states. We also obtain order alpha^5 corrections to the hyperfine splitting of the 1S and 2S levels.