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.

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.

The muon anomalous magnetic moment has been measured in a new experiment at Brookhaven. Polarized muons were stored in a superferric ring, and the angular frequency difference, v a , between the spin precession and orbital frequencies was determined by measuring the time distribution of highenergy decay positrons. The ratio R of v a to the Larmor precession frequency of free protons, v p , in the storage-ring magnetic field was measured. We find R 3.707 220͑48͒ 3 10 23. With m m ͞m p 3.183 345 47͑47͒ this gives a m 1 1 165 925͑15͒ 3 10 29 (613 ppm), in good agreement with the previous CERN measurements for m 1 and m 2 and of approximately the same precision.

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The spin precession frequency of muons stored in the (g − 2) storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for: a nonzero ∆ωa (=ω PACS numbers: 11.30.Cp, 11.30.Er, 13.40.Em, 12.20.Fv, 14.60.Ef The minimal standard model of particle physics is Lorentz and CPT invariant. Since the standard model is expected to be the low-energy limit of a more fundamental theory such as string theory that incorporates gravity, Lorentz and CPT invariance might be broken spontaneously in the underlying theory [1]. At low energies, the Lorentz and CPT violation signals are expected to be small but perhaps observable in precision experiments.To describe the effects of spontaneous breaking of Lorentz and CPT invariance, Colladay and Kostelecký [2] proposed a general standard model extension that can be viewed as the low-energy limit of a Lorentz covariant theory. Lorentz and CPT violating terms are introduced into the Lagrangian as a way of modeling the effect of spontaneous symmetry breaking in the underlying fundamental theory. Other conventional properties of quantum field theory such as gauge invariance, renormalizability and energy conservation are maintained, and the effective theory can be quantized by the conventional approach. In a subsequent paper, Bluhm, Kostelecký and Lane discussed specific precision experiments with muons that could be sensitive to the CPT and Lorentz violating interactions [3].In this letter we present our analysis for CPT and Lorentz violating interactions in the anomalous spin precession frequency, ω a , of the muon moving in a magnetic field. In experiment E821 [4] at the Brookhaven National Laboratory Alternating Gradient Synchrotron, muons are stored in a magnetic storage ring that uses electrostatic quadupoles for vertical focusing. The storage ring has a highly uniform magnetic field with a central value of B 0 = 1.45 T, and a central radius of ρ = 7.112 m. Polarized muons are injected into the storage ring, and the positrons (electrons) from the parityviolating decay µ +(−) → e +(−)ν µ (ν µ ) ν e (ν e ) carry average information on the muon spin direction at the time of the decay. Twenty-four electromagnetic calorimeters