• Fermilab
• g-2
• phase acceptance
• systematics

The measurement of the muon magnetic anomaly aµ = (gµ−2/2), where g is the g-factor of the muon, is one of the most accurate tests of the Standard Model (SM) theory of elementary particles. This quantity is known at a very high precision (∼ 0.5 parts per million), both theoretically and experimentally. Dirac’s equation predicts gµ = 2 and therefore aµ = 0, whereas SM radiative corrections, dominated by the QED Schwinger term α/2π ≈ 0.00116, predict aµ with a total accuracy of 0.5 ppm, with the main source of uncertainty coming from the QCD sector. The E821 experiment at Brookhaven National Laboratory in 2001 measured aµ with an accuracy of 0.54 ppm and found a tantalizing difference of 3.7 standard deviations compared to the SM prediction. The purpose of the new Muon g-2 experiment E989 at Fermilab is to reduce the total experimental error by a factor of 4 to 0.14 ppm, by achieving a statistical and a systematic error of comparable size (0.1 ppm). When a muon is injected into a magnetic field, both its spin and its momentum vectors precede, and, since aµ != 0, the rate at which the spin turns relative to the momentum is ωa = aµ(e/m)B, namely “anomalous precession frequency”. This means that aµ can be extracted by accurately measuring ωa and B. In E989 experiment, positive muons are injected at the so-called “magic momentum” of 3.1 GeV/c into a storage ring of 14 m of diameter, in the presence of a vertical dipolar magnetic field of 1.45 T, with an average bunch rate of 12 Hz. The choice of the magic momentum (γµ ≈ 29.3) is such that the electric field of the vertically focusing quadrupoles does not affect ωa. Due to parity violation in the weak process of muon decay, high energy positrons are emitted preferably towards the muon’s spin direction and can be detected by 24 electromagnetic calorimeters placed along the inner radius of the ring. Each calorimeter can measure the energy and the arrival time of emitted positrons and is made up of 6×9 crystals of lead fluoride (PbF2) read by silicon photomultipliers (SiPM). If we count all emitted positrons with an energy above 1.7 GeV as a function of time, the counting rate oscillates with ωa frequency and its maximum occurs when the muon spin and momentum vectors are aligned. ωa can therefore be extracted by fitting the histogram of the oscillating number of counted positrons as a function of time, called also wiggle plot, with a 22-parameter function, which takes into account, amongst others, detector and beam dynamics effects. Muons are stored in the ring for 700 µs (“fill time”), which corresponds to almost 5000 turns of the muon beam in the ring, and to about 160 periods of the anomalous precession (T of anom. prec. = 4.4 µs). All effects that change over this time-scale affect the ωa measurement and must be well-known and accounted for in the fitting procedure. The work of this Thesis consisted in the discussion of the systematic effects affecting the ωa extraction for the first run of data in 2018 (Run1). Chapter 1 introduces the subject of the anomalous magnetic moment of the muon. Chapter 2 describes the current status of the SM theoretical prediction, and reviews some possible New Physics scenarios. Chapter 3 reviews the history of the muon g −2 experiments and Chapter 4 gives an overview on the E989 experiment, focusing on the improvements that were necessary to reach the design goal on the measurement of aµ. Chapter 5 discusses the different sources of systematic error on ωa measurement, starting from the ones that originate from detector effects: Pileup, that occurs when two positrons hit the same calorimeter crystal very close in time, and Gain instability of the SiPMs during fill time. There are also systematic effects due to beam dynamics, that are parametrized in the fitting function: the Coherent Betatron Oscillation (CBO), both in the radial and vertical directions, and Lost Muons, which are muons that exit the storage ring due to their imperfect trajectory, lowering the number of emitted positrons during fill time. The so-called E-field and Pitch corrections affect ωa as well, because not all muons travel at the magic momentum and their trajectory is not always perpendicular to the magnetic field. Chapter 6, which is the original part of the Thesis, introduces the so-called “Phase Acceptance” (PA) effect, which, due to the limited calorimeter acceptance in the presence of magnetic field, affects the reconstructed phase of the muon spin when positrons are emitted from different beam positions around the ring. This effect, which is larger for Run1 due to damaged quadrupole resistors that affected RC time constants on beam dynamics parameters, fixed in Run2, turned out to be one of the largest and unexpected contribution to the ωa uncertainty. The analysis of the PA effect uses data from Run1 and from Monte Carlo simulation: many studies were performed to establish the size of the contribution on ωa and its uncertainty. For the whole Run1 dataset, the PA affects ωa at the level of O(100 ppb) with an uncertainty of ∼ 40 ppb, whereas, for Run2, preliminary studies showed that the impact of PA was less than 50 ppb.