Measurement of the muon anomalous precession frequency with the Run-2/3 data in the Muon g-2 experiment at Fermilab

The measurement of the muon magnetic anomaly a_μ=(g_μ−2)/2, where g_μ is the g-factor of the muon, is one of the most accurate tests of the Standard Model (SM) theory of elementary particles. Its theoretical value is dominated by the QED Schwinger term α/2π≈0.00116, but all sectors of the SM contribute to the interaction of muons with a magnetic field through virtual particles in quantum loops. On the experimental side, the anomaly can be measured very precisely, with a well-established technique. When muons are injected into a magnetic field, both their spin and their momentum vectors precess, and the precession frequency of the spin with respect to the momentum, the so-called "anomalous precession frequency", can be obtained as ω_a≡ a_μe/mB. This means that a_μ can be extracted by accurately measuring ω_a and B. In the Muon g−2 experiment at Fermilab (E989), a 3.1-GeV spin-polarized beam of positive muons is injected into a storage ring of 14m of diameter, in the presence of a 1.45T magnetic field. The experiment published a new result in 2023, based on the 2019 and 2020 data (namely Run-2/3), in very good agreement with the previous experimental results. From the combination, the new experimental world average is a_μ(Exp)=116592059(22)×10−11(0.19 ppm). The original work of this Thesis is presented in Chapters from 5 to 8: in particular, the "Ratio-Asymmetry" method, which was new with respect to Run-1, to analyze the anomalous ω_a frequency with Run-2/3 data. This method greatly reduces the sensitivity of ω_a to all slowly varying systematic effects, and it also achieves the maximum statistical power on ω_a by applying appropriate weights to the data. My results for ω_a were averaged with those from 5 other independent groups, to produce the final ω_a values and uncertainties that were published in 2023.