Measuring the anomalous precession frequency $\omega_a$ for the Muon $g-2$ Experiment

The magnetic anomaly of the muon $a_\mu$ hints at new physics with a greater than 3 standard deviation discrepancy between the measurement performed at Brookhaven National Lab and the Standard Model prediction. To clarify (or resolve) the disparity, the ongoing Muon $g-2$ Experiment at Fermilab has accrued a dataset larger than that of its predecessor experiment. The magnetic anomaly is directly proportional to the rate at which a muon's spin precesses relative to its momentum in a magnetic field, $\omega_a$. Decay positron energies, measured using 24 highly gain-stabilized calorimeters, carry information about the spin distribution of the parent muons; higher energy positrons are more likely emitted in the direction of the muons' spins. Determination of $\omega_a$ is made from fitting the time-dependent distribution of positron energies using several methods: setting a lower threshold on the positron energy; taking a ratio of time-shifted histograms; and an asymmetry weighting technique based on positron energies. Corrections must be made for muons that exit the storage region before decaying, beam betatron motions, and rate-dependent pileup in the detectors. The process of measuring $\omega_a$ and associated systematic errors will be presented in the context of Run 1 data.