Muonium Decay

TL;DR

This paper investigates how muonium formation and medium effects influence mu+ decay, revealing that most corrections cancel out, resulting in an extremely small lifetime difference between muonium and free mu+.

Contribution

The study demonstrates that medium effects on mu+ lifetime are highly suppressed and that the dominant bound state effect is an extremely small lifetime difference.

Findings

Corrections to muonium and mu+ decay spectra cancel at leading order.

The lifetime difference between muonium and free mu+ is approximately 6×10^-10.

Medium effects on mu+ lifetime are generally negligible due to suppression mechanisms.

Abstract

Modifications of the mu+ lifetime in matter due to muonium (M = mu+ e-) formation and other medium effects are examined. Muonium and free mu+ decay spectra are found to differ at O(alpha m_e/m_mu) from Doppler broadening and O(alpha^2 m_e/m_mu) 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, (tau_M - tau_mu+)/tau_mu+ = alpha^2 m_e^2/ 2m_mu^2 \simeq 6\times 10^-10, as the dominant bound state effect. It is argued that other medium effects on the stopped mu+ lifetime are similarly suppressed.