The Pitch and Electric Field Corrections to the Anomalous Muon Spin Precession Frequency for the Muon $g-2$ Experiment

The Muon $g-2$ Experiment (Fermilab E989) aims to measure the muon's anomalous magnetic moment, $a_\mu = (g_\mu-2)/2$, to a precision of 140 parts-per-billion (ppb). The measurement is performed by observing the anomalous spin precession frequency $\omega_a$ of a muon ensemble within a magnetic storage ring. The measured precession frequency is directly proportional to $a_\mu$, up to perturbations from two primary beam dynamics effects which must be corrected. One effect arises from vertical oscillations within a vertically focusing electric quadrupole field, called the pitch correction. Another arises from the quadrupoles' radial electric field, called the electric field correction. Both effects can perturb $\omega_a$ by hundreds of ppb, and must be carefully determined in order to reach the target precision for $a_\mu$. Here we present the methodology and results for the pitch and electric field corrections from the experiment's Run-1 measurement period.