Bound states of the muon-antimuon system: Lifetimes and hyperfine splitting

We examine the properties of an atomic system consisting of a muon and antimuon. Expressions are derived for the probability of decay and the hyperfine splitting of the lower levels with allowance for the leading radiative corrections, which are of relative order α. The results for the lifetimes and the ground-state energy are τ(13 S 1)=1.7907(8)×10−12 s, τ(11 S 0)=0.59547(33)×10−12 s, and E hfs (1s)=4.23284(35)×107 MHz. The relative probabilities for the various decay channels are calculated; in particular, for the 1 3 S 1 level it is found that Γ (μμ→eeγ)/Γ(μμ→ee)≈15%. Finally, possible applications are discussed.