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(αm_e/m_μ) from Doppler broadening and O(α²m_e/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⁺=α²m_e²/2m_μ²≃6×10^-10, as the dominant bound state effect. It is argued that other medium effects on the stopped μ⁺ lifetime are similarly suppressed.