We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a µ = (g − 2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a µ (Expt) = 11 659 208.0(5.4)(3.3) × 10 −10 , where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a µ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ≈ 0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e + e − hadronic cross sections, lie 2.2 -2.7 standard deviations below the experimental result.

The anomalous magnetic moment of the negative muon has been measured to a precision of 0.7 ppm (ppm) at the Brookhaven Alternating Gradient Synchrotron. This result is based on data collected in 2001, and is over an order of magnitude more precise than the previous measurement for the negative muon. The result a(mu(-))=11 659 214(8)(3) x 10(-10) (0.7 ppm), where the first uncertainty is statistical and the second is systematic, is consistent with previous measurements of the anomaly for the positive and the negative muon. The average of the measurements of the muon anomaly is a(mu)(exp)=11 659 208(6) x 10(-10) (0.5 ppm).

Three independent searches for an electric dipole moment (EDM) of the positive and negative muons have been performed, using spin precession data from the muon g À 2 storage ring at Brookhaven National Laboratory. Details on the experimental apparatus and the three analyses are presented. Since the individual results on the positive and negative muons, as well as the combined result, d ¼ ð0:0 AE 0:9Þ Â 10 À19 e cm, are all consistent with zero, we set a new muon EDM limit, jd j < 1:8 Â 10 À19 e cm (95% C.L.). This represents a factor of 5 improvement over the previous best limit on the muon EDM.

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A higher precision measurement of the anomalous g value, aµ = (g − 2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron, based on data collected in the year 2000. The result a µ + = 11 659 204(7)(5) × 10 −10 (0.7 ppm) is in good agreement with previous measurements and has an error about one half that of the combined previous data. The present world average experimental value is aµ(exp) = 11 659 203(8) × 10 −10 (0.7 ppm). The study of magnetic moments has played an important role in our understanding of sub-atomic physics. Precision measurements of the electron anomalous magnetic moment, together with those of the hyperfine structure of hydrogen and the Lamb shift, stimulated the development of modern quantum electrodynamics and have since provided stringent tests of this theory. In this Letter we report a new measurement of the anomalous magnetic moment of the positive muon, a µ = (g − 2)/2, with a relative precision of 0.7 parts per million (ppm), nearly two times better than our previous work [1,2,3]. This measurement comes from data collected in the year 2000. At this level, a µ is sensitive to QED, weak, and hadronic virtual loops and provides an important constraint on extensions to the standard model.The principle of the experiment and previous results have been given in earlier publications [1,2,3]. Also, detailed descriptions of the (g − 2) superconducting inflector magnet, storage ring magnet, fast kicker, NMR system, and calorimeters have been published [4].The quantity a µ is determined fromThe magnetic field B weighted over the muon beam distribution is measured by proton NMR. The difference frequency ω a between the muon spin precession and orbital angular frequencies is determined by counting the number N (t) of decay positrons with energies larger than an energy threshold,The normalization N 0 , asymmetry A, and phase φ a vary with the chosen threshold. The time dilated lifetime is γτ ≈ 64.4 µs. For muons with γ = 29.3, the angular difference frequency ω a is not affected by electrostatic focusing fields in the ring. New aspects of the 2000 data taking period include: the operation of the AGS with 12 beam bunches, contributing to a 4-fold increase in data collected as compared to 1999; a new superconducting inflector magnet, which improved the field homogeneity in the muon storage region; the installation and operation of a sweeper magnet in the beamline, which reduced AGS background; and additional muon loss detectors, which enable an improved determination of the time dependence of muon losses. Most other experimental aspects of the data taking in 2000 were the same as in 1998 and 1999.The magnetic field value was obtained from NMR measurements of the free proton resonance frequency. A trolley with 17 NMR probes was used to measure the field