ar X iv : h ep - p h / 99 08 43 9 v 1 2 3 A ug 1 99 9 BNL - HET - 99 / 20 , hep - ph / 9908439 Muonium Decay

Muonium (M = μe) bound state effects are shown to decrease the muon decay rate by a factor of 1 − 5αme/mμ = 0.9999987. That small 1.3 ppm shift is near the sensitivity of proposed muon lifetime measurements. The annihilation rate Γ(M → νeν̄μ) is also computed and found to be ≃ 6.6 × 10Γ(μ → eνeν̄μ). Other potential medium effects on stopped muon decay are briefly discussed. The muon lifetime, τμ, is very well measured. Its current world average [1] τμ = 2.197035(40)× 10 sec (1) exhibits an uncertainty of only 20 ppm. From that lifetime, the Fermi constant (denoted here by Gμ) is determined via the defining relationship [2–4] τ μ = Γ(μ→ all) = G2μm 5 μ 192π f (