Boundμ+μ−system

Abstract

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 ${10}^{-12}$ s 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 timelike 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 ${\alpha }^5{m}_{\mu }$ corrections to the hyperfine splitting of the $1S$ and $2S$ levels.