Abstract

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 $\omega_a^m$.

Highlights

  • This paper presents the beam dynamics systematic corrections and their uncertainties for the Run-1 dataset of the Fermilab Muon g − 2 Experiment

  • The measurement of the muon magnetic anomaly1 aμ ≡ ðg − 2Þ=2, where gμ is the factor describing the relationship of the muon magnetic moment to its spin, has undergone significant development since the late 1960s when the idea of using a magnetic storage ring for the measurement was first introduced [1]

  • Two storage ring experiments at CERN [1,2] and the Brookhaven National Laboratory (BNL) Experiment (E821) [3] have increasingly refined the technique, leading to a determination of aμ to a precision of 0.54 ppm [3]. These experiments determine aμ by measuring the muon spin precession frequency relative to the momentum vector while a muon beam is confined in a storage ring

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Summary

Introduction

The measurement of the muon magnetic anomaly aμ ≡ ðg − 2Þ=2, where gμ is the factor describing the relationship of the muon magnetic moment to its spin, has undergone significant development since the late 1960s when the idea of using a magnetic storage ring for the measurement was first introduced [1]. Two storage ring experiments at CERN [1,2] and the Brookhaven National Laboratory (BNL) Experiment (E821) [3] have increasingly refined the technique, leading to a determination of aμ to a precision of 0.54 ppm [3]. These experiments determine aμ by measuring the muon spin precession frequency relative to the momentum vector while a muon beam is confined in a storage ring. The Fermilab Muon g − 2 Experiment (E989) is designed to test the validity of the BNL result and to go further by improving on the experimental precision

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