Analysis of the Anomalous Spin Precession of the Muon for the Fermilab Muon g-2 Experiment

Abstract

The E989 Muon $g-2$ Experiment at Fermilab searches for signals of physics beyond the standard model by precisely measuring the anomalous magnetic moment of the muon ($a_{\mu}$) and comparing the result to the standard model prediction. The measurement of $a_{\mu}$ can be broken into three components: measurement of the anomalous spin precession frequency of the muon ($\omega_{a}$), measurement of the magnetic field of the $g-2$ storage ring using proton NMR, and characterization of the dynamic motion of the muon beam. Recently published results from Runs 2 and 3 of the experiment have increased the precision on the world average value of $a_{\mu}$ by a factor of two to 0.19 parts-per-million (ppm). These results are in strong tension with a 2020 evaluation of $a_{\mu}$ in the standard model. This thesis describes the work to analyze the remaining data (Runs 4-6) of the Muon $g-2$ experiment. These datasets represent $73$% of the total data collected and are expected to bring the final experimental uncertainty to $\leq 0.14$ ppm. An overview of the $g-2$ experiment is presented, with special attention paid to the precession frequency measurement hardware and the analysis chain through which the $\omega_{a}$ data is processed and collated into `physics-quality' datasets. A preliminary analysis of the Run-4 $\omega_{a}$ data follows, which yields by itself a statistical precision of $0.19$ ppm. Finally, selected systematic studies and remaining analysis work are presented and discussed.