Beam dynamics corrections to the Run-1 measurement of the muon anomaly $a_μ$ at Fermilab

Abstract: The Fermi National Accelerator Laboratory (FNAL) Muon $g-2$ Experiment has measured the positive muon magnetic anomaly $a_{\mu} \equiv (g_{\mu}-2)/2$ with a precision of 0.46 parts per million, with data collected during its first physics run in 2018. The experimental result combined with the measurement from the former experiment at Brookhaven National Laboratory increases the tension with the Standard Model expectation to $4.2\sigma$, thus strengthening evidence for new physics. The magnetic anomaly is determined from the precision measurements of the muon spin precession frequency, relative to the muon momentum, and the average magnetic field seen by the beam. In an ideal case with muons orbiting in a horizontal plane with a uniform vertical magnetic field, the anomalous precession frequency $\omega_a$ is given by the difference between the spin~($s$) and cyclotron~($c$) frequencies, $\omega_a = \omega_s - \omega_c$. The observable $\omega_a$ is proportional to $a_{\mu}$. This proceeding presents the beam dynamics systematic corrections that are required to adjust the measured muon precession frequency $\omega^{m}_{a}$ to its true physical value $\omega_{a}$.