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

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 $\omega_a^m$

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 $\omega_a^m$

Observational Review and Analysis of Concussion: a Method for Conducting a Standardized Video Analysis of Concussion in Rugby League

Background: Several professional contact and collision sports have recently introduced the use of sideline video review for club medical staff to help identify and manage concussions. As such, reviewing video footage on the sideline has become increasingly relied upon to assist with improving the identification of possible injury. However, as yet, a standardized method for reviewing such video footage in rugby league has not been published. The aim of this study is to evaluate whether independent raters reliably agreed on the injury characterization when using a standardized observational instrument to record video footage of National Rugby League (NRL) concussions. Methods: Video footage of 25 concussions were randomly selected from a pool of 80 medically diagnosed concussions from the 2013–2014 NRL seasons. Four raters (two naïve and two expert) independently viewed video footage of 25 NRL concussions and completed the Observational Review and Analysis of Concussion form for the purpose of this inter-rater reliability study. The inter-rater reliability was calculated using Cohen’s kappa (κ) and intra-class correlation (ICC) statistics. The two naïve raters and the two expert raters were compared with one another separately. Results: A considerable number of components for the naïve and expert raters had almost perfect agreement (κ or ICC value ≥ 0.9), 9 of 22 (41%) components for naïve raters and 21 of 22 (95%) components for expert raters. For the concussion signs, however, the majority of the rating agreement was moderate (κ value 0.6–0.79); both the naïve and expert raters had 4 of 6 (67%) concussion signs with moderate agreement. The most difficult concussion sign to achieve agreement on was blank or vacant stare, which had weak (κ value 0.4–0.59) agreement for both naïve and expert raters. Conclusions: There appears to be value in expert raters, but less value for naive raters, in using the new Observational Review and Analysis of Concussion (ORAC) Form. The ORAC Form has high inter-rater agreement for most data elements, and it can be used by expert raters evaluating video footage of possible concussion in the NRL

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 aμ(gμ-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 ωp′, the denominator in the ratio ωa/ωp′ that together with known fundamental constants yields aμ. The reported uncertainty on ωp′ 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