O(α3lnα)Corrections to Muonium and Positronium Hyperfine Splitting

Abstract
We compute O(α3lnα) relative corrections to the ground-state hyperfine splitting of a QED two-body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon-to-electron mass ratio is derived from the muonium ground-state hyperfine splitting.