Year: 2000
Type: article
Abstract: Modifications of the ${\ensuremath{\mu}}^{+}$ lifetime in matter due to muonium $(M={\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}})$ formation and other medium effects are examined. Muonium and free ${\ensuremath{\mu}}^{+}$ decay spectra are found to differ at $\mathcal{O}(\ensuremath{\alpha}{m}_{e}{/m}_{\ensuremath{\mu}})$ from Doppler broadening and $\mathcal{O}({\ensuremath{\alpha}}^{2}{m}_{e}{/m}_{\ensuremath{\mu}})$ 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, $({\ensuremath{\tau}}_{M}\ensuremath{-}{\ensuremath{\tau}}_{{\ensuremath{\mu}}^{+}})/{\ensuremath{\tau}}_{{\ensuremath{\mu}}^{+}}={\ensuremath{\alpha}}^{2}{m}_{e}^{2}{/2m}_{\ensuremath{\mu}}^{2}\ensuremath{\simeq}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10},$ as the dominant bound state effect. It is argued that other medium effects on the stopped ${\ensuremath{\mu}}^{+}$ lifetime are similarly suppressed.
Institution: Brookhaven National Laboratory
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3037553807