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.

A precise measurement of the anomalous g value, aµ = (g − 2)/2, for the positive muon has been made at the Brookhaven Alternating Gradient Synchrotron. The result a µ + = 11 659 202(14)(6) × 10 −10 (1.3 ppm) is in good agreement with previous measurements and has an error one third that of the combined previous data. The current theoretical value from the standard model is aµ(SM)= 11 659 159.6(6.7) × 10 −10 (0.57 ppm) and aµ(exp)−aµ(SM) = 43(16) × 10 −10 in which aµ(exp) is the world average experimental value.PACS number: 14.60.Ef 13.40.EmPrecise measurement of the anomalous g value, a µ = (g−2)/2, of the muon provides a sensitive test of the standard model of particle physics and new information on speculative theories beyond it. Compared to the electron, the muon g value is more sensitive to standard model extensions, typically by a factor of (m µ /m e ) 2 . In this Letter we report a measurement of a µ for the positive muon from Brookhaven AGS experiment 821, based on data collected in 1999.The principle of the experiment, previous results, and many experimental details have been given in earlier publications [1,2]. Briefly, highly polarized µ + of 3.09 GeV/c from a secondary beamline are injected through a superconducting inflector [3] into a storage ring 14.2 m in diameter with an effective circular aperture 9 cm in diameter. The superferric storage ring [4] has a homogeneous magnetic field of 1.45 T, which is measured by an NMR system relative to the free proton NMR frequency [5,6]. Electrostatic quadrupoles provide vertical focusing. A pulsed magnetic kicker gives a 10 mrad deflection which places the muons onto stored orbits. The muons start in 50 ns bunches and debunch with a decay time of about 20 µs due to their 0.6% momentum spread. Positrons are detected using 24 lead/scintillating fiber electromagnetic calorimeters [7] read out by waveform digitizers. The waveform digitizer and NMR clocks were phase-locked to the Loran C frequency signal.The muon spin precesses faster than its momentum rotates by an angular frequency ω a in the magnetic field B weighted over the muon distribution in space and time. The quantity a µ iswhere ω a is unaffected by the electrostatic field for muons with γ = 29.3. Parity violation in the decay µ + → e +ν µ ν e causes positrons to be emitted with an angular and energy asymmetry. Because of the Lorentz boost, the positron emission angle with respect to the muon spin direction in the muon rest frame is strongly coupled to its energy in the laboratory frame. The number of decay positrons with energy greater than E is described byin which the time dilated lifetime γτ ≈ 64.4 µs. Some 140 g − 2 periods of 4.37 µs were observed. Most experimental aspects of the data taking in 1999 were the same as in 1998 [1]. However, some improvements were made. Care was taken in tuning the AGS ejection system to minimize background from any extraneous proton beam extracted during the muon storage time. Scintillating fiber detectors which could be moved in and out of the storage region were u...

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 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

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