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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mulan: a part-per-million measurement of the muon lifetime and determination of the Fermi constant

The part-per-million measurement of the positive muon lifetime and determination of the Fermi constant by the MuLan experiment at the Paul Scherrer Institute is reviewed. The experiment used an innovative, time-structured, surface muon beam and a near-4 \pi π , finely-segmented, plastic scintillator positron detector. Two in-vacuum muon stopping targets were used: a ferromagnetic foil with a large internal magnetic field, and a quartz crystal in a moderate external magnetic field. The experiment acquired a dataset of 1.6 \times 10^{12} 1.6 × 10 12 positive muon decays and obtained a muon lifetime \tau_{\mu} = 2\, 196\, 980.3(2.2) τ μ = 2 196 980.3 ( 2.2 ) ~ps (1.0~ppm) and Fermi constant G _F = 1.166\, 378\, 7(6) \times 10^{-5} F = 1.166 378 7 ( 6 ) × 10 − 5 GeV ^{-2} − 2 (0.5~ppm). The thirty-fold improvement in \tau_{\mu} τ μ has proven valuable for precision measurements in nuclear muon capture and the commensurate improvement in G _F F has proven valuable for precision tests of the standard model.

Carey, Rebecca↗
DOE OSTI2021

Overview of SoLID

SoLID spectrometer was proposed to fully exploit the potential of JLab 12 GeV energy upgrade. It is a large acceptance detector which can handle very high luminosity. An overview of the rich physics program will be given, which includes number of planned measurements: a multi-dimensional mapping of semi-inclusive DIS asymmetries for tomography of the nucleon in momentum space in the high-x region and precision determination of the tensor charge; a measurement of parity-violating DIS to provide a precision test of the Standard Model, reaching a sensitivity to new physics at 10-20 TeV level; a precision measurement of J/psi photo- and electro-production cross sections in the threshold region to probe the strong color fields in the nucleon and to study the origin of the proton mass. The current status and the plan of the project will be discussed.

Chen, Jian-Ping↗
DOE OSTI2022

Measurement of the anomalous spin precession frequency $\omega_a$ in the Muon $g-2$ experiment at Fermilab

The muon anomaly, $a_\mu=(g_{\mu}-2)/2$, is a low-energy observable which can be both measured and computed to high precision, making it a sensitive test of the Standard Model (SM) and a probe for new physics. The current discrepancy between the experimental value and the Standard Model calculation from the Muon $g-2$ Theory Initiative is $a_{\mu}^{exp}-a_{\mu}^{SM}=(251\pm59)\cdot10^{-11}$, with a significance of $4.2\,\sigma$.The Fermilab E989 experiment aims, with the full statistical power, to improve by a factor of four the precision of the measurement.In April 2021 the collaboration published the first measurement, based on the first year of data taking.This paper will present the status of the measurement of the anomalous muon spin precession frequency, $\omega_a$, performed on the datasets collected during Run-2 and Run-3 (2019 and 2020 campaigns), with a preliminary projection of the systematic uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Status and prospects of Muon g-2 experiment

This article reviews the muon g-2 experiment, a cornerstone in precision tests of the Standard Model of particle physics. The experiment measures the anomalous magnetic moment of the muon with unprecedented accuracy, seeking potential discrepancies between theoretical predictions and experimental results that might indicate physics beyond the Standard Model. We trace the evolution of this measurement from its beginnings at CERN in the 1960s to the current state-of-the-art experiment at Fermilab, highlighting the remarkable engineering achievements required to achieve parts-per-billion precision. Recent results from Runs 1-3 have achieved a systematic uncertainty of 70 ppb, exceeding design goals, while ongoing theoretical calculations continue to refine predictions. Despite these advances, the analysis remains statistics-limited, with continued data collection and novel experimental approaches at MUonE and J-PARC promising further insights into this fundamental physical quantity.

Karuza, Marin [INFN, Trieste; Rijeka U.] (ORCID:00↗
DOE OSTI2020

Weak Transitions in Light Nuclei

Nuclei are used for high-precision tests of the Standard Model and for studies of physics beyond the Standard Model. Without a thorough understanding of nuclei, we will not be able to meaningfully interpret the growing body of experimental data nor will we be able to disentangle new physics signals from underlying nuclear effects. This calls for accurate calculations of nuclear structure and reactions. In this work, we focus on electroweak decays in nuclei with mass number A ≤ 10 and report on ab initio Quantum Monte Carlo calculations of reduced matrix elements entering beta decays and electron captures in nuclei with mass number A ≤ 10. The many-body wave functions are calculated using selected Norfolk two- and three-nucleon potential models and associated one- and two-body axial currents at tree-level obtained from a chiral effective field theory with pions, nucleons, and Δ. The agreement with the experimental data is satisfactory except for transitions in A = 8 nuclei. In this specific case, the theory significantly underpredicts the experimental data, which indicates the need of further improvements in the corresponding nuclear wave functions. In this study, emphasis is placed on the contributions of two-body axial currents that are carefully analyzed using two-body transition densities. This allow us to study the spatial distribution and short-range behavior of two-body dynamics. In particular, the transition densities when scaled to peak at 1.0 exhibit universal short-range behavior across the considered nuclei, while they differ in the long-range tails.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Strong Interaction Dynamics and Fermi $β$ Decay in the Nucleon and the Nucleus

Nuclear super-allowed β decay has been used to obtain tight limits on the value of the CKM matrix element V ud that is important for unitarity tests and, therefore, for tests of the standard model. Current requirements on precision are so intense that effects formerly thought too small to matter are now considered relevant. This article is a brief review of personal efforts to include the effects of strong interactions on Fermi β decay. First, I examine the role of isospin violation in the decay of the neutron. The size of the necessary correction depends upon detailed strong-interaction dynamics. The isospin violating parts of the nucleon wave function, important at the low energy of β decay, can be constrained by data taken at much higher energies, via measurements, for example, of ed → e'π ± + X reactions at Jefferson Laboratory. The next point of focus is on the role of nuclear short-ranged correlations, which affect the value of the correction needed to account for isospin violation in extracting the value of V ud . The net result is that effects previously considered as irrelevant are now considered relevant for both neutron and nuclear β decay.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Modeling Solids in Nuclear Astrophysics with Smoothed Particle Hydrodynamics

Abstract Smoothed particle hydrodynamics (SPH) is a frequently applied tool in computational astrophysics to solve the fluid dynamics equations governing the systems under study. For some problems, for example when involving asteroids and asteroid impacts, the additional inclusion of material strength is necessary in order to accurately describe the dynamics. In compact stars, that is white dwarfs and neutron stars, solid components are also present. Neutron stars have a solid crust, which is the strongest material known in nature. However, their dynamical evolution, when modeled via SPH or other computational fluid dynamics codes, is usually described as a purely fluid dynamics problem. Here, we present the first 3D simulations of neutron star crustal toroidal oscillations including material strength with the Los Alamos National Laboratory SPH code FleCSPH. In the first half of the paper, we present the numerical implementation of solid material modeling together with standard tests. The second half is on the simulation of crustal oscillations in the fundamental toroidal mode. Here, we dedicate a large fraction of the paper to approaches that can suppress numerical noise in the solid. If not minimized, the latter can dominate the crustal motion in the simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier

An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron–Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Searching for Clues for a Matter Dominated Universe in Liquid Argon Time Projection Chambers

Liquid Argon Time Projection Chambers (LArTPCs) represent one of the most widely utilized neutrino detection techniques in neutrino experiments, for instance, in the Short Baseline Neutrino (SBN) program and the future large-scale LArTPC: Deep Underground Neutrino Experiment (DUNE). The high-end technique, facilitating excellent spatial and calorimetric reconstruction resolution, also enables testing exotic Beyond Standard Model (BSM) theories, such as baryon number violation (BNV) processes (e.g., proton-decay, neutron-antineutron oscillation). At the same time, Machine Learning (ML) techniques have demonstrated their ubiquitous use in recent decades; ML techniques have also become some of the most powerful tools in high-energy physics (HEP) analyses. Furthermore, the development of algorithms to cater to the needs of problems in HEP (i.e., triggering, reconstruction, improving sensitivity, etc.) has also become an active area of research. By developing a combined approach using Convolutional Neural Network (CNN) and Boosted Decision Tree (BDT) techniques, the sensitivity of neutron-antineutron oscillation in DUNE is evaluated for a projected exposure of 400kton·years. Additionally, to meet the triggering requirement to select such rare events in DUNE, such a search is only supported with highly efficient self-triggering algorithms. An ML-based self-triggering scheme for large-scale LArTPCs, such as DUNE, is also developed with the intention of implementation on field-programmable gate arrays (FPGAs). The ML-based approach for searching for neutron-antineutron oscillation can be demonstrated and validated on the current LArTPC MicroBooNE. The analysis in MicroBooNE represents the first-ever search for neutron-antineutron oscillation in a LArTPC. DUNE's projected 90% C.L. sensitivity to the neutron antineutron oscillation lifetime is 6.45×10³² years, assuming 1.327×10³⁵ neutron·years, equivalent to 10 years of DUNE far detector exposure (400kton·years). For MicroBooNE, assuming 372 seconds of exposure (equivalent to 3.13×10³⁶ neutron·years), the 90% C.L. lifetime sensitivity is found at 3.07×10²⁵ yrs, after accounting for Monte-Carlo statistical uncertainty and systematic uncertainty from detector effects.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1981

Fracture mechanics of cellular glass

The fracture mechanics of cellular glasses (for the structural substrate of mirrored glass for solr concentrator reflecting panels) are discussed. Commercial and developmental cellular glasses were tested and analyzed using standard testing techniques and models developed from linear fracture mechanics. Two models describing the fracture behavior of these materials were developed. Slow crack growth behavior in cellular glass was found to be more complex than that encountered in dense glasses or ceramics. The crack velocity was found to be strongly dependent upon water vapor transport to the tip of the moving crack. The existence of a static fatigue limit was not conclusively established, however, it is speculated that slow crack growth behavior in Region 1 may be slower, by orders of magnitude, than that found in dense glasses.

Zwissler, J. G.↗
NASA NTRS1983

Fracture mechanics of cellular glass

The fracture mechanics of cellular glasses (for the structural substrate of mirrored glass for solar concentrator reflecting panels) are discussed. Commercial and developmental cellular glasses were tested and analyzed using standard testing techniques and models developed from linear fracture mechanics. Two models describing the fracture behavior of these materials were developed. Slow crack growth behavior in cellular glass was found to be more complex than that encountered in dense glasses or ceramics. The crack velocity was found to be strongly dependent upon water vapor transport to the tip of the moving crack. The existence of a static fatigue limit was not conclusively established, however, it is speculated that slow crack growth behavior in Region 1 may be slower, by orders of magnitude, than that found in dense glasses. Previously announced in STAR as N82-11209

Zwissler, J. G.↗
NASA NTRS2013

XIPE the X-Ray Imaging Polarimetry Explorer

X-ray polarimetry, sometimes alone, and sometimes coupled to spectral and temporal variability measurements and to imaging, allows a wealth of physical phenomena in astrophysics to be studied. X-ray polarimetry investigates the acceleration process, for example, including those typical of magnetic reconnection in solar flares, but also emission in the strong magnetic fields of neutron stars and white dwarfs. It detects scattering in asymmetric structures such as accretion disks and columns, and in the so-called molecular torus and ionization cones. In addition, it allows fundamental physics in regimes of gravity and of magnetic field intensity not accessible to experiments on the Earth to be probed. Finally, models that describe fundamental interactions (e.g. quantum gravity and the extension of the Standard Model) can be tested. We describe in this paper the X-ray Imaging Polarimetry Explorer (XIPE), proposed in June 2012 to the first ESA call for a small mission with a launch in 2017. The proposal was, unfortunately, not selected. To be compliant with this schedule, we designed the payload mostly with existing items. The XIPE proposal takes advantage of the completed phase A of POLARIX for an ASI small mission program that was cancelled, but is different in many aspects: the detectors, the presence of a solar flare polarimeter and photometer and the use of a light platform derived by a mass production for a cluster of satellites. XIPE is composed of two out of the three existing JET-X telescopes with two Gas Pixel Detectors (GPD) filled with a He-DME mixture at their focus. Two additional GPDs filled with a 3-bar Ar-DME mixture always face the Sun to detect polarization from solar flares. The Minimum Detectable Polarization of a 1 mCrab source reaches 14 in the 210 keV band in 105 s for pointed observations, and 0.6 for an X10 class solar flare in the 1535 keV energy band. The imaging capability is 24 arcsec Half Energy Width (HEW) in a Field of View of 14.7 arcmin 14.7 arcmin. The spectral resolution is 20 at 6 keV and the time resolution is 8 s. The imaging capabilities of the JET-X optics and of the GPD have been demonstrated by a recent calibration campaign at PANTER X-ray test facility of the Max-Planck-Institut fr extraterrestrische Physik (MPE, Germany). XIPE takes advantage of a low-earth equatorial orbit with Malindi as down-link station and of a Mission Operation Center (MOC) at INPE (Brazil). The data policy is organized with a Core Program that comprises three months of Science Verification Phase and 25 of net observing time in the following 2 years. A competitive Guest Observer program covers the remaining 75 of the net observing time.

Astronomy X-ray Polarimetry↗
DOE OSTI2021

Status of the Fermilab Muon g - 2 Experiment

The muon anomalous magnetic moment, aµ = ( g - 2 )/2, is a low-energy observable which can be both measured and computed with very high precision, making it an excellent test of the Standard Model (SM) and a sensitive probe of new physics. Recent efforts improved the precision of both the theoretical prediction and the experimental measurement. On the theory side, the Muon g - 2 Theory Initiative, an international team of more than 130 physicists, reached in 2020 a consensus on the SM prediction for aµ. On the experimental side, the E989 Muon g - 2 Collaboration at Fermilab (FNAL) published in April 2021 a new measurement of aµ from the Run-1 dataset (2018) with 0.46 ppm precision, corroborating the previous Brookhaven National Laboratory (BNL) measurement and increasing the discrepancy with the SM value to 4.2 standard deviations. In this paper, I will discuss the experimental setup and report on the current status of the experiment.

Girotti, Paolo↗
DOE OSTI2022

The Muon g-2 Experiment at Fermilab

The muon magnetic anomaly, $a_{\mu}$, is a powerful test of the Standard Model of particle physics. A new experiment at Fermilab has recently measured $a_{\mu}$ with unprecedented precision, confirming the results of the earlier Brookhaven experiment and strengthening the tension with the prediction of the Standard Model as determined by dispersive methods. We here describe the experimental technique, recapitulate the recent result, and discuss some of the improvements made for subsequent analyses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Muon Campus at Fermilab

The Muon Campus at Fermilab provides world class accelerator infrastructure supporting the next generation intensity frontier experiments. The anti-proton source from the Tevatron era was converted to the present day Muon Campus at the end of the collider program in 2011. Currently, the Muon Campus delivers highly polarized muon beams to the Muon g-2 experiment and in a few years, it will provide muon beams to the Mu2e experiment. The Muon g-2 experiment is a high precision test of the standard model; it is precise enough to measure QED, Weak, and QCD Standard Model contributions.The Muon g-2 experiment looks for a significant deviation from the Standard Model whereas the Mu2e experiment looks for rare processes using high intensity muon beams. The Muon g-2 experiment has measured the anomalous magnetic moment of muons to an unprecedented 460 ppb precision with Run 1 data. The experiment has completed 5 runs, accumulating 19$\times$ Brookhaven E821 data set. The Mu2e experiment has completed the construction phase and first beam to the Diagnostic Absorber was run on April 14, 2022. Installation and commissioning of the Mu2e experiment will begin in 2023 and beam commissioning and physics run is currently planned for 2026.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

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

The anomalous magnetic moment of the muon, $a_\mu = \frac{g-2}{2}$ is the fractional deviation of the muon $g$-factor from the value of 2. It emerges as the cumulative effect of the virtual particles participating in the muon interaction with a magnetic field via quantum loop corrections. Its value encodes all the possible interactions between the virtual particles and, for this reason, represents an important test of the Standard Model (SM). In particular, any deviation from the SM theoretical evaluation could be due to new physics contributions. 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 (Run-1), measuring $a_\mu = 0.001~165~920~40(54)$ 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 4.2$\sigma$. 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. The E989 collaboration is now finalizing the analysis of Run-2 and Run-3 data and a new publication is expected in the first half of 2023 with a combined statistical uncertainty of 200 ppb. The anomalous magnetic moment $a_\mu$ is measured as the ratio between the muon spin anomalous precession frequency, $\omega_a$, and the average magnetic field experienced by the muons as they circulate in the storage ring. 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 $\omega_a$ 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 $a_\mu$ result is presented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Measurement of the muon spin precession frequency using the straw tracking detectors at the Fermilab Muon g-2 experiment

The measurement of the anomalous magnetic dipole moment of the muon ($a_{\mu}$) has long stood as an excellent precision test of the Standard Model (SM). The Fermilab Muon g-2 experiment has recently finished data-taking and in July 2023 published its latest determination of $a_\mu$ with a world-leading precision of 0.2\,ppm. In this publication, it surpassed the systematic uncertainty goal defined in the TDR. The analyses of a dataset approximately four times larger than this recent publication is now underway. The principle measurement of the Muon g-2 experiment measures $a_{\mu}$ by taking the ratio of two frequencies; the anomalous precession frequency ($\omega_a$) and the muon-weighted magnetic field of the experiment's storage ring measured from the precession frequency of protons in water using nuclear magnetic resonance (NMR) probes. In all publications to date, $\omega_a$ has been determined using energy deposits in the 24 calorimeters. However, the Fermilab experiment has t wo straw tracker detectors measuring the time and momentum of charged particles which can in principle also be used to to measure $\omega_a$ and such a measurement can provide an invaluable cross-check of the calorimeter result with different, and reduced, systematic uncertainties. This thesis presents the first (blinded) determination of $\omega_a$ using just charged tracks from the straw tracking detectors as opposed to calorimeter energy deposits. This analysis was undertaken using the Run-2/3 dataset which represents approximately 25\% of the final dataset. A total uncertainty of 2.19\,ppm on $\omega_a$ was obtained which is dominated by the statistical uncertainty of 2.16\,ppm. Additionally two new methodologies important to the analysis of the straw tracking data have been developed: one to better determine the track arrival time ($t_0$) and one to determine the level of pileup in the tracking detectors. The new $t_0$ algorithm which incorporates angular information improves t he resolution on the determination of the $t_0$ by a factor of two and results in 19\% more tracks being successfully reconstructed. The data from the trackers is also used to determine the beam profile that weights the magnetic field in the determination of $a_\mu$ and in determining several of the systematic uncertainties in the calorimeter-based $\omega_a$ analysis. A detailed study of the impact of the internal alignment of the tracker, the $t_0$ and pileup on the determination of the beam position was undertaken and propagated through to an uncertainty in the $\omega_a$ determination. These uncertainties were used in the Fermilab Muon g-2 experiment's recent publication in Phys. Rev. Lett.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Beam dynamics corrections in the measurement of the anomalous precession frequency at the Muon $g-2$ experiment at Fermilab

The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗