Alignment of the straw tracking detectors for the Fermilab Muon $g-2$ experiment and systematic studies for a muon electric dipole moment measurement

The Fermilab Muon g􀀀2 experiment is currently preparing for its fourth datataking period (Run-4). The experiment-wide effort on the analysis of Run-1 data is nearing completion, with the announcement of the first result expected in the coming months. The final goal of the experiment is to determine the muon magnetic anomaly, a = g􀀀2 2 , to a precision of 140 ppb. This level of precision will provide indirect evidence of new physics, if the central value agrees with the previously-measured value of a. Essential in reducing the systematic uncertainty on a, through measurements of the muon beam profile, are the in-vacuum straw tracking detectors. A crucial prerequisite in obtaining accurate distributions of the beam profile is the internal alignment of the tracking detectors, which is described in this thesis. As a result of this position calibration, the tracking efficiency has increased by 3%, while the track quality increased by 4%. This thesis also discusses an additional measurement that will be made using the tracking detectors: a search for an electric dipole moment (EDM) of the muon, through the direct detection of an oscillation in the average vertical angle of the e+ from the + decay. An observation of a muon EDM would be evidence of new physics and would provide a new source of CP violation in the charged lepton sector. Essential in measuring the EDM, as well as a, are accurate and precise estimations of potential non-zero radial and longitudinal magnetic fields, which were estimated using the Run-1 data. In addition, a preliminary analysis using the Run-1 data was undertaken to estimate the available precision for the a measurement using the tracking detectors. 3