Beam dynamics corrections to the measured anomalous precession frequency in the Fermilab muon g-2 experiment.

The Fermilab Muon $g-2$ experiment has measured $a_\mu$ with an unprecedented precision of 127 ppb designed to determine the muon’s magnetic moment anomaly, $a_\mu$. This anomaly is extracted from the ratio of the muon’s anomalous spin precession frequency within a magnetic storage ring to the magnetic field experienced by the ensemble of muons. However, the measured precession frequency is subject to systematic biases arising from muon beam dynamics. In the analysis, two primary categories of systematic effects are considered: (i) reductions in the spin precession frequency due to electric fields and vertical motion, and (ii) variations in the precession phase over the course of the muon $fill$ period. In this paper, we describe the beam dynamics corrections applied to the $a_\mu$ measurement of data collected from 2020 to 2023 (Run-456) and quantify the size of these corrections for the experiment’s final result.