Evaluation of Systematic Uncertainties in the Precise Magnetic Field Measurement for the Muon g-2 Experiment

The Fermilab E989 Muon g-2 experiment's goal is to measure the anomalous magnetic dipole moment of the muon, $a_\mu$ with a precision of 140 ppb to test the prediction of $a_\mu$ in the Standard Model (SM) of subatomic physics. The Brookhaven National Laboratory (BNL) experiment E821, the most recent previous muon g-2 measurement, produced a result in 2005 with a precision of 0.54 ppm, that differed by 3.5 to 3.7 $\sigma$ from the SM prediction. After more than 10 years, Fermilab E989 continued the BNL measurement, taking the first physics data in 2018. At the time of this writing, Run 6 is ongoing and measurements of Runs 1 through Run 5 are completed. The targeted 4-fold improvement in precision would yield an above 5 sigma tension assuming the central values don't change, opening the possibility of discovery of physics beyond the Standard Model.

To reach the goal of 140 ppb, E989 aims for 100 ppb statistical and 100 ppb systematical uncertainties. In order to measure $a_\mu$, there are two major observables needed: $\omega_a$, the anomalous precession frequency, and $\Tilde{\omega}'_p$, the average magnetic field weighted by the muon distribution around the 14-meter diameter storage ring, determined at a 70 ppb level. The field is precisely mapped using a field mapper, which carries 17 NMR probes, running around the muon storage region every 2 or 3 days. Calibration of these 17 NMR probes to the absolute probe, in-situ water-based calibration probe, is crucial for accurate measurements. The field's drift between the field maps is tracked using 378 NMR probes installed at fixed positions around the outside of the muon storage ring. The result of the Run 1 dataset was published in April 2021 and agreed with the BNL experiment. Analysis of Run 2 and 3 data is nearing completion as of this writing. This dissertation discusses the experiment, and detailed methods applied in evaluating the systematic uncertainties for the magnetic field measurement with a focus on Run 2 and 3.