A new approach for measuring the muon anomalous magnetic moment and electric dipole moment

This paper introduces a new approach to measure the muon magnetic moment anomaly a?? = (g - 2)/2 and the muon electric dipole moment (EDM) d?? at the J-PARC muon facility. The goal of our experiment is to measure a?? and d?? using an independent method with a factor of 10 lower muon momentum, and a factor of 20 smaller diameter storage-ring solenoid compared with previous and ongoing muon g - 2 experiments with unprecedented quality of the storage magnetic field. Additional significant differences from the present experimental method include a factor of 1000 smaller transverse emittance of the muon beam (reaccelerated thermal muon beam), its efficient vertical injection into the solenoid, and tracking each decay positron from muon decay to obtain its momentum vector. The precision goal for a?? is a statistical uncertainty of 450 parts per billion (ppb), similar to the present experimental uncertainty, and a systematic uncertainty less than 70 ppb. The goal for EDM is a sensitivity of 1.5 ?? 10-21 ecm

Beam dynamics corrections to the Run-1 measurement of the muon anomalous magnetic moment at Fermilab

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 ωam 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 ω_{a}^{m} is 0.50±0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of ω_{a}^{m}

Magnetic-field measurement and analysis for the Muon g − 2 Experiment at Fermilab

The Fermi National Accelerator Laboratory (FNAL) Muon g - 2 Experiment has measured the anomalous precession frequency a_{μ}(g_{μ} - 2)/2 of the muon to a combined precision of 0.46 parts per million with data collected during its first physics run in 2018. This paper documents the measurement of the magnetic field in the muon storage ring. The magnetic field is monitored by systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7C. The measured field is weighted by the muon distribution resulting in \tilde{ω}'_{p}, the denominator in the ratio \tilde{ω}_{a}/\tilde{ω}'_{p} that together with known fundamental constants yields aμ. The reported uncertainty on \tilde{ω}'_{p} for the Run-1 data set is 114 ppb consisting of uncertainty contributions from frequency extraction, calibration, mapping, tracking, and averaging of 56 ppb, and contributions from fast transient fields of 99 ppb

Muon (g-2) Technical Design Report

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

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.20 ppm

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

Learning environment, attitudes and anxiety across the transition from primary to secondary school mathematics

Past research has revealed that, relative to primary-school students, high-school students have less-positive attitudes to mathematics and perceive their classroom environments and teacher–student relationships less favourably. This study involved the transition experience of 541 students in 47 classes in 15 primary (year 7) and secondary (year 8) government and Catholic schools in metropolitan and regional South Australia. Scales were adapted from three established instruments, namely, the What Is Happening In this Class?, Test of Mathematics Related Attitudes and Revised Mathematics Anxiety Ratings Scale, to identify changes across the transition from primary to secondary school in terms of the classroom learning environment and students’ attitude/anxiety towards mathematics. Relative to year 7 students, year 8 students reported less Involvement, less positive Attitude to Mathematical Inquiry, less Enjoyment of Mathematics and greater Mathematics Anxiety. Differences between students in Years 7 and 8 were very similar for male and female students, although the magnitude of sex differences in attitudes was slightly different in Years 7 and 8

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.Comment: Contribution to Snowmass 2021; updated with community edits and endorsement

Measurement of the anomalous precession frequency of the muon in the Fermilab Muon g-2 Experiment

The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency $\omega_a$ to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of $a_{\mu}({\rm FNAL}) = 116\,592\,040(54) \times 10^{-11}$ (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the eleven separate determinations of \omega_a, and the systematic uncertainties on the result.Comment: 29 pages, 19 figures. Published in Physical Review