New Theoretical Prediction of the Ground-State Hyperfine Splitting in Muonium

Abstract

We have computed a new contribution to the ground-state hyperfine splitting in muonium: $\ensuremath{-}2{(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{2}(\frac{m}{M}){[\mathrm{ln}(\frac{M}{m})]}^{2}$ ${E}_{F}=\ensuremath{-}6.6$ kHz. Uncalculated theoretical contributions are expected to be no larger than a few kHz. The new theoretical estimate, ${\ensuremath{\nu}}_{\mathrm{theor}}=4463297.9(7.0)$ kHz is in good agreement with experiment: ${\ensuremath{\nu}}_{\mathrm{expt}}=4463302.35(0.52)$ kHz. The bulk of the uncertainty in the theory is due to uncertainty in the measured value of $\frac{{\ensuremath{\mu}}_{\ensuremath{\mu}}}{{\ensuremath{\mu}}_{p}}$.