Muon mass ratio

The sum of the main Fermi contribution and the Breit correction is given in the last line of Table 9.1. The uncertainty of the main Fermi contribution determines the uncertainty of the theoretical prediction of HFS in the ground state in muonium, and is in its turn determined by the experimental uncertainty of the electron-muon mass ratio. 

The agreement between theory and experiment is excellent. However, the error bars of the theoretical value are apparently about an order of magnitude larger than respective error bars of the experimental result. This is a deceptive impression. The error of the theoretical prediction in (12.31) is dominated by the experimental error of the value of the electron-muon mass ratio. As a result of the latest experiment [83] this error was reduced threefold but it is still by far the largest source of error in the theoretical value for the muonium hyperfine splitting. 

One can use high accuracy of the hyperfine splitting theory, and highly precise experimental result in (12.33) in order to obtain the value of the Fermi energy much more precise than the one in (12.30). But according to (8.2) the Fermi energy is proportional to the electron-muon mass ratio, and we can extract this mass ratio from the experimental value of HFS and the most precise value of a... 

---