Precession frequency analysis for Run-2 and Run-3 of the Muon g-2 experiment

Abstract

The Fermilab Muon $g-2$ experiment aims to measure the anomalous magnetic momentum of the muon, $a_{\mu}$, to 140 part per billion precision. This measurement is compared to the Standard Model (SM) value for $a_{\mu}$ as a precision test of the SM. The result of the first run of data taking was published in April 2021 and verified the results of the previous experiment at Brookhaven National Laboratory. The average measured value of $a_{\mu}$ now stands in tension with the official Standard Model calculation to 4.2$\sigma$. The anomalous magnetic moment $a_{\mu}$ is measured by taking the ratio of two frequencies: the anomalous precession frequency $\omega_a$, which is the difference between the spin and cyclotron precession frequencies of a muon in a magnetic storage ring, and $\tilde{\omega}_p$, which is the muon-weighted storage ring magnetic field as measured by the precession frequency of protons in nuclear magnetic resonance probes. This thesis presents a precession frequency analysis of the second and third data taking runs, which have a combined statistical uncertainty of 200 ppb, more than twice as precise as the Run-1 measurement. A summary of the data preparation for fitting will be described, including an update to the algorithm used to reconstruct decay positron information from the detectors. Then, the fitting procedure used to extract $\omega_a$ will be discussed. Finally, the systematic uncertainties associated with the precession frequency analysis will be analyzed.