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

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

Magnetic Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab

The Fermi National Accelerator Laboratory has measured the anomalous precession frequency $a^{}_\mu = (g^{}_\mu-2)/2$ 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 nuclear magnetic resonance systems and calibrated in terms of the equivalent proton spin precession frequency in a spherical water sample at 34.7$^\circ$C. The measured field is weighted by the muon distribution resulting in $\tilde{\omega}'^{}_p$, the denominator in the ratio $\omega^{}_a$/$\tilde{\omega}'^{}_p$ that together with known fundamental constants yields $a^{}_\mu$. The reported uncertainty on $\tilde{\omega}'^{}_p$ 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

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 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ 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 $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$

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 data set of the Fermilab Muon g-2 Experiment. Two corrections to the measured muon precession frequency $\omega_a^m$ 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 $\omega_a^m$ is 0.50 $\pm$ 0.09 ppm; the uncertainty is small compared to the 0.43 ppm statistical precision of $\omega_a^m$

A Measurement Of The Solar And Sidereal Cosmic-ray Anisotropy At E0 ∼ 1014 Ev

The results of the measurement of the cosmic-ray solar and sidereal anisotropies at primary energy E0 ≈ 1014 eV performed by the EAS-TOP Extensive Air Shower array (Campo Imperatore, National Gran Sasso Laboratories, 2005 m above sea level, latitude 42°.5 N are presented. The measurement includes 4 years of data taking (1990, 1992, 1993, 1994) for a total of 1.3 × 109 events and is performed at two different mean primary energies: E0v ≈ 1.5 × 1014 eV and E0i ≈ 2.5 × 1014 eV. The two results are compatible (within 2 σ) and can therefore be combined. The obtained amplitude and phase of the first harmonic in sidereal time are (in the equatorial plane) Asid, δ=0, (E0 ≈ 2 × 1014 eV) = (3.73 ± 0.57) × 10-4 and sid = 1.82 ± 0.49 hr local sidereal time, with significance 6.5 a. The amplitude of the anisotropy exhibits the expected cos δ dependence. A first harmonic in solar time compatible with the expected Compton-Getting effect due to the motion of revolution of the Earth around the Sun is observed with significance 7.3 σ. The corresponding measured amplitude and phase (also in the equatorial plane) are Asol, δ=0° = (4.06 ± 0.55) × 10-4 and sol = 4.92 ± 0.53 hr, the expected values being 4.7 × 10-4 and 6.0 hr. Different checks of stability of the detectors and consistency of the data are presented. © 1996. The American Astronomical Society. All rights reserved.4701 PART I501505Aglietta, M., (1986) Nuovo Cimento, 9 C, p. 262. , EAS-TOP Collaboration(1993) Proc, 23d Int. Cosmic-Ray Conf. (Calgary), 2, p. 65(1993) Nucl. Instrum. Methods a, 336, p. 310(1993) Proc. 23d Int. Cosmic-Ray Conf. (Calgary)., 4, p. 247(1995) Proc. 24th Int. Cosmic-Ray Conf. (Rome), 2, p. 800Alexeenko, V.V., (1981) Proc. 17th Int. Cosmic-Ray Conf. (Paris), 2, p. 146(1993) Proc. 23d Int Cosmic-Ray Conf. (Calgary), 1, p. 483Andreyev, Y., (1987) Proc. 20th Int Cosmic-Ray Conf. (Moscow), 2, p. 22Bergamasco, L., (1990) Proc. 21st Int. Cosmic-Ray Conf. (Adelaide), 6, p. 372Compton, A.H., Getting, I.A., (1935) Phys. Rev., 47, p. 817(1995) Proc. 24th Int Cosmic-Ray Conf. (Rome), 2, p. 732Parley, F.J.M., Storey, J.R., (1954) Proc. Phys. Soc., A, 67, p. 996Fenton, A.G., (1976) Proc. International Cosmic-Ray Symposium on High-energy Cosmic-Ray Modulation, p. 313. , ed. Cosmic-Ray Laboratory (Tokyo:Univ. Tokyo)Gombosi, T., (1975) Nature, 255, p. 687Kiraly, P., (1979) Nuovo Cimento, 2, p. 7Linsey, J., (1983) Proc. 18th Int. Cosmic-Ray Conf. (Bangalore), 12, p. 135Nagashima, K., (1989) Nuovo Cimento, 12, p. 69