Measurement of the muon anomalous precession frequency at the Muon g-2 Experiment at Fermilab

The anomalous magnetic moment of the muon is the fractional deviation of the muon g-factor from the value of 2. Its value represents an important test of the Standard Model (SM). The new Muon g-2 (E989) Experiment at Fermilab is currently operating to repeat and improve the previous E821 experiment at Brookhaven National Laboratory (BNL), aiming to reduce the experimental error by a factor of 4 to the final accuracy of 140 parts per billion (ppb). On April 7th, 2021, the E989 collaboration published the first result based on the first year of data taking with a precision of 460 ppb. The measured value is consistent with the BNL measurement and strengthens the long-standing tension with the data-driven SM prediction to a combined discrepancy of 4.2σ. On the theory side, however, new efforts involving lattice-QCD techniques are starting to question the current consensus on the theoretical prediction, demanding new improvements on both the experimental and theoretical sides. This thesis presents a precession frequency analysis of the Run-1 data and an evaluation of the related systematic uncertainties. A new positron reconstruction developed for the analysis of the subsequent data-taking periods, aiming to reduce some of the major systematic uncertainties of the precession measurement, is presented. The author's involvement in the production of the Run-2/5 data and in the precise calibration of the detectors is discussed. Finally, the complete Run-1 aµ result is presented.