Muonium decay

Modifications of the μ⁺ lifetime in matter due to muonium (M=μ⁺e^-) formation and other medium effects are examined. Muonium and free μ⁺ decay spectra are found to differ at O(αmₑ/m_μ) from Doppler broadening and O(α²mₑ/m_μ) from the Coulomb bound state potential. However, both types of corrections are shown to cancel in the total decay rate due to Lorentz and gauge invariance respectively, leaving a very small time dilation lifetime difference, $({{τ}}M{-}{{τ}}_{{{μ}}⁺})/{{τ}}_{{{μ}}⁺}={{α}}²{m}ₑ²{/2m}_{{μ}}²{}6×{}{10}^{{-}10},$ as the dominant bound state effect. It is argued that other medium effects on the stopped ${{μ}}⁺$ lifetime are similarly suppressed.