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

Understand

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.