Measurement of the anomalous magnetic moment of the negative muon to 0.7 parts per million

The present generation of measurements of the anomalous magnetic moment of the muon (a_μ) have reached sub part per million (ppm) precision, a level at which they are sensitive to electromagnetic and hadronic interactions, and for the first time, to the electroweak interactions. Comparing the experimental results with Standard Model evaluations provides stringent constraints on physics beyond our current model. The determination of a_μ at Experiment 821 at Brookhaven National Laboratory requires simultaneous measurements of the muon spin precession frequency and the magnetic field of the muon storage ring. This analysis, one of several to measure the spin precession frequency, uses a ratio of phase-shifted decay electron time spectra to unshifted time spectra. Combined with an independent measurement of the magnetic field, the anomalous magnetic moment of the negative muon has now been determined to a precision of 0.7 parts per million (ppm): a_μ− = 11659214(8)(3) × 10−10. This value is in good agreement with measurements of the anomalous magnetic moment of the positive muon: a_μ+ = 11659204(7)(5) × 10−10 (0.7 ppm). We discuss the principle of and the analysis techniques used in this experiment, and compare the final results with the theoretical prediction for a_μ.