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

TL;DR

This paper details the systematic beam dynamics corrections applied to the Fermilab Muon g-2 Run-1 data, refining the measurement of the muon anomalous magnetic moment with minimal uncertainty.

Contribution

It introduces new correction methods for beam dynamics effects in the muon g-2 experiment, improving the precision of the precession frequency measurement.

Findings

Total correction to the precession frequency is 0.50 ppm.

Uncertainty in corrections is 0.09 ppm, smaller than statistical error.

Corrections account for motional magnetic fields, pitch angles, and beam drift effects.

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 $\omega_a^m$.