Magnetic Moment of the Positive Muon

The magnetic moment of the positive muon has been measured relative to that of the proton by determining its precession frequency in a magnetic field measured by proton NMR. With both protons and muons bound in a spherical sample of water, the result is $\frac{{\omega }_{{\mu }^{\prime }}}{{\omega }_{p^{\prime }}}=3.183\mathrm{}362\pm 0.000030$ (9.4 ppm). Including uncertainties due to the chemical environment of the muon, the result for free muons and protons is $\frac{{\omega }_{\mu }}{{\omega }_p}=3.183\mathrm{}330\pm 0.000044$ (14 ppm) which is consistent with recent measurements of the hyperfine splitting of muonium.