We present a new measurement of the positive muon magnetic anomaly, a_{μ}≡(g_{μ}-2)/2, from the Fermilab Muon g-2 Experiment using data collected in 2019 and 2020. We have analyzed more than 4 times the number of positrons from muon decay than in our previous result from 2018 data. The systematic error is reduced by more than a factor of 2 due to better running conditions, a more stable beam, and improved knowledge of the magnetic field weighted by the muon distribution, ω[over ˜]_{p}^{'}, and of the anomalous precession frequency corrected for beam dynamics effects, ω_{a}. From the ratio ω_{a}/ω[over ˜]_{p}^{'}, together with precisely determined external parameters, we determine a_{μ}=116 592 057(25)×10^{-11} (0.21 ppm). Combining this result with our previous result from the 2018 data, we obtain a_{μ}(FNAL)=116 592 055(24)×10^{-11} (0.20 ppm). The new experimental world average is a_{μ}(exp)=116 592 059(22)×10^{-11} (0.19 ppm), which represents a factor of 2 improvement in precision.

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g-2 Experiment for the positive muon magnetic anomaly a_{μ}≡(g_{μ}-2)/2. The anomaly is determined from the precision measurements of two angular frequencies. Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω_{a} between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring. The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω[over ˜]_{p}^{'} in a spherical water sample at 34.7 °C. The ratio ω_{a}/ω[over ˜]_{p}^{'}, together with known fundamental constants, determines a_{μ}(FNAL)=116 592 040(54)×10^{-11} (0.46 ppm). The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement. After combination with previous measurements of both μ^{+} and μ^{-}, the new experimental average of a_{μ}(Exp)=116 592 061(41)×10^{-11} (0.35 ppm) increases the tension between experiment and theory to 4.2 standard deviations.

This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon g - 2 Experiment. Two corrections to the measured muon precession frequency omega(m)(a) are associated with well-known effects owing to the use of electrostatic quadrupole (ESQ) vertical focusing in the storage ring. An average vertically oriented motional magnetic field is felt by relativistic muons passing transversely through the radial electric field components created by the ESQ system. The correction depends on the stored momentum distribution and the tunes of the ring, which has relatively weak vertical focusing. Vertical betatron motions imply that the muons do not orbit the ring in a plane exactly orthogonal to the vertical magnetic field direction. A correction is necessary to account for an average pitch angle associated with their trajectories. A third small correction is necessary, because muons that escape the ring during the storage time are slightly biased in initial spin phase compared to the parent distribution. Finally, because two high-voltage resistors in the ESQ network had longer than designed RC time constants, the vertical and horizontal centroids and envelopes of the stored muon beam drifted slightly, but coherently, during each storage ring fill. This led to the discovery of an important phase-acceptance relationship that requires a correction. The sum of the corrections to omega(m)(a) is 0.50 +/- 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of omega(m)(a).

The anomalous magnetic moment of the muon is one of the most precisely measured quantities in experimental particle physics. Its latest measurement at Brookhaven National Laboratory deviates from the Standard Model expectation by approximately 3.5 standard deviations. The goal of the new experiment, E989, now under construction at Fermilab, is a fourfold improvement in precision. Here, we discuss the details of the future measurement and its current status.

The Muon (g-2) Experiment, E989 at Fermilab, will measure the muon anomalous magnetic moment a factor-of-four more precisely than was done in E821 at the Brookhaven National Laboratory AGS. The E821 result appears to be greater than the Standard-Model prediction by more than three standard deviations. When combined with expected improvement in the Standard-Model hadronic contributions, E989 should be able to determine definitively whether or not the E821 result is evidence for physics beyond the Standard Model. After a review of the physics motivation and the basic technique, which will use the muon storage ring built at BNL and now relocated to Fermilab, the design of the new experiment is presented. This document was created in partial fulfillment of the requirements necessary to obtain DOE CD-2/3 approval.

Received 7 February 2011DOI:https://doi.org/10.1103/PhysRevLett.106.079901© 2011 American Physical Society

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 - 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(mu) = (0.0 +/- 0.9) x 10(-19)e cm, are all consistent with zero, we set a new muon EDM limit, vertical bar d(mu)vertical bar < 1.8 x 10(-19)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 delta omega a(=omega a mu+ - omega a mu-) and a sidereal variation of omega a mu+/-). No significant effect is found, and the following limits on the standard-model extension parameters are obtained: bZ = -(1.0+/-1.1) x 10(-23) GeV; (m mu dZ0 + HXY)=(1.8+/-6.0) x 10(-23) GeV; and the 95% confidence level limits b perpendicular mu+ <1.4 x 10(-24) GeV and b perpendicular mu- <2.6 x 10(-24) GeV.

In the muon (g-2) experiment at Brookhaven National Laboratory, the spin precession frequency ωa is obtained from a standard χ2 minimization fit applied to the time distribution of decay electrons. The unusually high accuracy (∼0.5ppm) of the experiment puts stringent requirements on the quality of the fit and the level of understanding of the statistical properties of the fitted parameters. We discuss the properties of the fits and their implications on the derived value for ωa, including estimates of the effect of an imperfect fit function, methods of including additional external information to reduce the error, the effects of splitting the data into many smaller subsets of data, applying different weighting methods to the data using energy information, and various tests of data suitability.

We report results from the MuLan measurement of the positive muon lifetime. The experiment was conducted at the Paul Scherrer Institute using a time-structured surface muon beam and a segmented plastic scintillator array. Two different in-vacuum muon stopping targets were used: a ferromagnetic foil with a large internal magnetic field and a quartz crystal in a moderate external magnetic field. From a total of 1.6 x 10^12 decays, we obtained the muon lifetime tau_mu = 2196980.3(2.2) ps (1.0 ppm) and Fermi constant G_F = 1.1663787(6) x 10^-5 GeV^-2 (0.5 ppm).

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a(mu)=(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(mu)(Expt)=11659208.0(5.4)(3.3)x10(-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(mu) includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, approximate to 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.

We present the final report from a series of precision measurements of the muon anomalous magnetic moment, aμ = (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 aμ(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 aμ 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 E821 Collaboration measured the muon anomalous magnetic moment aμ to a precision of 0.54 ppm. It differs from standard model theory by 2.4 standard deviations. We propose to carry out an upgraded effort at the AGS to reach a precision of ±0.2 ppm, a factor of 2.5 improvement. This step forward will be well matched to anticipated advances in the worldwide effort to determine the standard model theoretical value for aμ . With the anticipated improved theory value, the future experiment-theory comparison would have an uncertainty of ≈ 4 − 5 × 10−10, allowing stringent tests of standard model extensions. The principal feature of the new experiment is a redesigned pion / muon beamline that will deliver a significantly higher muon flux and eliminate the hadronic flash at injection. The higher statistical sample will require a new detector, electronics and data acquisition system and a reduction in the major systematic uncertainties. This proposal outlines a plan to carry out this experiment—at BNL—making optimum use of the considerable investment in the E821 storage ring and associated experimental elements. Because the major changes planned do not require extensive R&D, we can be ready for a commissioning run two years after approval and funding, and ready for a production run approximately one year later. We request a period of “pulse on demand” running using fast extraction to the V-line, followed by 3 weeks of engineering running. A major data collection run of 21 weeks would follow one year after the engineering run.

In this paper a new method is presented for particles in storage rings which could reach a statistical sensitivity of 10−27 e⋅cm for the deuteron EDM. This implies an improvement of two orders of magnitude over the present best limits on the T‐odd nuclear forces ξ parameter.

The muon (g-2) experiment is described, and the recent results are presented. These results represent the final measurement for the positive muon.

The g-factor of the muon differs from two due to the excitation of virtual field quanta and particles. The deviation from two, the g-factor anomaly, can be calculated with high precision in the Standard Model of particle physics. The g-factor anomaly can be measured with high precision by determining the rate at which the spin direction of high-energy muons circulating in a storage ring precesses. The Brookhaven National Laboratory g−2 experiment (BNL g−2 collaboration) has measured g−2 to 1.3ppm. The result is essentially in agreement with the Standard Model. The result puts interesting constraints on Standard Model extensions. Data under analysis will reduce the uncertainty to the order of 0.5ppm. The precision timing techniques used in the g−2 experiment are a central element of a new experiment to measure the lifetime of the positive muon. The goal of this experiment is to determine the lifetime to 1ppm, and the Fermi coupling constant to 0.5ppm. The high statistics demand of this measurement is satisfied by one of the surface muon beams of the Paul Scherrer Institute. An artificial time structure is imposed on the continuous beam by an electrostatic kicker. The decay positrons are detected in a 180 element quasi-spherical detector. The effective counting rate is of the order of 1MHz. The experiment is designed to control systematic errors to a level below 1ppm.

A description is given of a new experiment to measure the muon electric dipole moment (EDM) to between sigma = 10(-24) e-cm and 10(-25) e-cm, which would be 5 to 6 orders of magnitude improvement over the current world average. Muons are stored in a magnetic ring. Precession due to Thomas precession and the magnetic moment are canceled with the proper combination of applied E and B fields. Only precession due to a non-vanishing EDM remains, resulting in a large amplification of the EDM signal. The method has general applicability to charged particles.

1 Department of Physics, Boston University, Boston, MA 02215, USA 2 Brookhaven National Laboratory, Upton, NY 11973, USA 3 Budker Institute of Nuclear Physics, Novosibirsk, Russia 4 Newman Laboratory, Cornell University, Ithaca, NY 14853, USA 5 Department of Physics, University of Illinois at Urbana-Champaign, IL 61801, USA 6 KEK, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0801, Japan 7 Kernfysisch Versneller Instituut, Rijksuniversiteit Groningen, NL 9747 AA Groningen, The Netherlands 8 Department of Physics, University of Minnesota, Minneapolis, MN 55455, USA Department of Physics, Osaka University, Toyonaka, Osaka, Japan 560-0043 Muon Science Laboratory, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan 11 Department of Physics, Yale University, New Haven, CT 06511, USA

The measurement of the (g-2) value of leptons provides a unique test of theory since it is the only quantity (unlike charge and mass) calculable in the framework of the Standard Model of elementary particles. The muon (g-2) experiment E821 is currently in progress at Brookhaven National Laboratory. Four data taking runs for positive muons and one run for negative unions were successfully accomplished in 1997-2000 and 2001, respectively. Results of the 1997-2000 runs have been published, thus completing our experiment for mu(+). Data analysis for the 2001 run for mu(-) is currently in progress. To provide measurement of a(mu)- = 1/2(g-2)(mu)- at the same level of accuracy as for a(mu)+ = 1/2(g-2)(mu)+, we need to have one more data taking run.