Measurement of the muon anomalous precession frequency ωₐ in the Fermilab Muon $g-2$ experiment

The Fermilab Muon $g-2$ Experiment was designed to measure the muon's anomalous magnetic moment aμ = (g-2)/2 to 140 parts per billion. The value of aμ is proportional to the difference frequency ωₐ=ωₛ-ωc between the muon's cyclotron frequency and spin precession frequency in the uniform magnetic field of the $g-2$ storage ring. The frequency ωₐ is extracted from the time distribution of the mu-decay positrons recorded by 24 electromagnetic calorimeters positioned around the inner circumference of the storage ring. We will discuss the various approaches to the frequency determination including the reconstruction, fitting of time distributions, and procedures for handling the effects of gain changes, positron pileup and beam dynamics. We also discuss the data consistency checks and the strategy for the averaging of ωₐ across the different analyses.