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DOE OSTI2018

Extraction of the Muon Revolution Frequency Distribution via the Fourier Analysis of the Fast Rotation Signal in the Muon g-2 Experiment

The Muon g-2 experiment at Fermi National Accelerator Laboratory aims to measure the anomalous magnetic moment a of the muon to an unprecedented precision of 0.14 ppm, obtaining a near four-fold increase in precision over the previous experiment at Brookhaven National Laboratory (BNL). The value of a from BNL diers from the Standard Model prediction by 3.4 standard deviations, suggesting a tantalizing hint of new physics and so motivating a new measurement. The Fermilab experiment follows the measurement principle from the BNL experiment. A beam of positive muons is stored in the ring, where a combination of magnetic and electric elds helps to focus the beam. The combination of these elds and the stored beam properties directly impact the nal extraction of of a. The muon anomaly relies on the measurement of the spin precession frequency !a about the momentum of the muon. Due to a muon beam momentum spread of approximately 0:1%, !a must be corrected for the eect of a radial electric eld. The correction is estimated by means of a modied Fourier analysis of the so-called fast rotation signal. We explore the application of this analysis to the case of a beam with longitudinal spread and to the case of late-time beam detection. We also consider the numerical extension of the method, and apply it to data from the recent commissioning run.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

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 data-taking 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 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 the magnetic anomaly. Essential in reducing the systematic uncertainty, 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 electron from the muon decay. An observation of a muon EDM would be evidencemore » of new physics and would provide a new source of CP violation in the charged lepton sector. Essential in measuring the EDM 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 magnetic anomaly measurement using the tracking detectors.« less

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Precision Measurement of the Muon Spin Precession Frequency in the Fermilab Muon g-2 Experiment

The Fermilab Muon $g-2$ Experiment is designed to measure the muon's anomalous magnetic moment, $ a_\mu = (g-2)/2 $ with an accuracy of 140 parts per billion. This quantity is determined from two key measurements; the difference between the muon's spin precession frequency and its cyclotron frequency, given by $\omega_a = \omega_s - \omega_c$, and $\tilde{\omega_p^\prime}$, proportional to the muon-weighted magnetic field.In this talk, we focus on presenting the methodology for determining $\omega_a$. Muons with a momentum of 3.1 GeV are injected into a storage ring, and $\omega_a$ is extracted from the time distribution of decay positrons recorded by 24 electromagnetic calorimeters placed symmetrically inwards around the ring. We present the final result from the muon g-2 collaboration and analysis techniques based on data collected from 2020 to 2023.

Zaid, Estifa'a [Liverpool U.]↗

NASA NTRS1985

On muon energy spectrum in muon groups underground

A method is described which was used to measure muon energy spectrum characteristics in muon groups underground using mu-e decays recording. The Baksan Telescope's experimental data on mu-e decays intensity in muon groups of various multiplicities are analyzed. The experimental data indicating very flat spectrum does not however represent the total spectrum in muon groups. Obviously the muon energy spectrum depends strongly on a distance from the group axis. The core attraction effect makes a significant distortion, making the spectrum flatter. After taking this into account and making corrections for this effect the integral total spectrum index in groups has a very small depencence on muon multiplicity and agrees well with expected one: beta=beta (sub expected) = 1.75.

Bakatanov, V. N.↗

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 OSTI2023

Measurement of the muon anomalous precession frequency in runs 2 \& 3 of the Muon $g-2$ Experiment at Fermilab

This dissertation presents a measurement of the muon anomalous precession frequency for the Runs 2 \& 3 data of the E989 Muon $g-2$ Experiment at Fermilab. The muon anomalous precession frequency is one of two key inputs, the other being the magnetic field, used to precisely determine the muon magnetic anomaly, $a_{\mu}$. In April 2021, the E989 collaboration reported its first measurement of $a_{\mu}$ to an unprecedented precision of 460 parts-per-billion (ppb). This result is in agreement with the previous measurement performed by the E821 collaboration at Brookhaven National Laboratory, and the combined experimental value is in tension with the Standard Model prediction at 4.2$\sigma$, a possible hint of new physics. The first result from E989 was based on the Run-1 data, which was collected in 2018 and comprises 6\% of the experiment’s target statistics; the Run-1 result was statistics-limited. The Runs 2 \& 3 data were collected in 2019-2020 and constitute a four-fold increase i n statistics compared to Run-1 and consequently, a factor of two reduction in the measurement’s statistical uncertainty. This reduced statistical uncertainty, as well as continued understanding of systematic effects, will result in an even more precise measurement of $a_{\mu}$ and will help clarify the observed tension between theory and experiment. The precession frequency analysis presented in this dissertation includes a number of improvements compared to Boston University's Run-1 analysis: the implementation of a more robust pileup-subtraction procedure, the implementation of a kernel ratio method, the adoption of the statistically optimal asymmetry-weighted method, and investigations that led to an improved understanding of an outstanding residual slow effect. This dissertation motivates a measurement of the muon magnetic anomaly, describes the experimental principle, gives an overview of the E989 experiment, and presents a precession frequency analysis with full systematic unc ertainty evaluation for the Runs 2 \& 3 data. The combined precession frequency measurement, using the ratio asymmetry-weighted method, has a statistical uncertainty of 201 ppb and a systematic uncertainty of 25 ppb, constituting the most precise determination of the muon anomalous precision frequency to date.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Precision test of the muon-Higgs coupling at a high-energy muon collider

We explore the sensitivity of directly testing the muon-Higgs coupling at a high-energy muon collider. This is strongly motivated if there exists new physics that is not aligned with the Standard Model Yukawa interactions which are responsible for the fermion mass generation. We illustrate a few such examples for physics beyond the Standard Model. With the accidentally small value of the muon Yukawa coupling and its subtle role in the high-energy production of multiple (vector and Higgs) bosons, we show that it is possible to measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeV muon collider and a few percent for a 30 TeV machine by utilizing the three boson production, potentially sensitive to a new physics scale about Λ ~ 30 - 100 TeV.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Lepton flavor violation: From muon decays to muon colliders

We investigate the unique potential of a high-energy muon collider to probe lepton-flavor-violating signals arising from physics beyond the Standard Model (SM). Low-energy, precision searches for charged lepton flavor violation (LFV) are projected to dramatically improve their sensitivity in the coming years and could provide the first evidence of new physics. We interpret the sensitivity of these searches in terms of a set of LFV operators in the SM effective field theory. The same operators are then probed at the TeV scale via new, high-energy processes only available at a high-energy muon collider, such as 𝜇⁢𝜇 → 𝜇⁢𝜏 or the scattering of a muon of an electroweak gauge boson into LFV final states. We find that, for most operators, a muon collider could confirm signals if they are seen at future low-energy experiments, whereas for certain flavor combinations it extends the reach to scales well beyond those accessible at lower energies. We also project the sensitivity of a muon collider to lepton-flavor-violating decays of the SM Higgs boson and demonstrate improved sensitivity to ℎ → 𝑒⁢𝜏 and ℎ → 𝜇⁢𝜏 by an order of magnitude compared to the High-Luminosity LHC. The importance of having multiple, complementary probes is illustrated by considering both various combinations of operators and relative sizes of flavor-violating transitions between generations under various assumptions for the flavor structure of new physics.

Asadi, Pouya [University of California, Santa Cruz↗

DOE OSTI2023

A Collaboration Website for Muon Catalyzed Fusion and Muon Beam Production

This project sets up a website to support the nascent Muon Catalyzed Fusion collaboration including development of particle accelerators and transport beamlines for muon beams. The website is envisioned as having the general public information pages and private pages for collaboration members. Multimedia elements like images, text animations, and video lectures, covering a broad spectrum of topics will populate the educational site, covering muon facilities, to comprehensive explorations and seminal documents that define the science of Muon Catalyzed Fusion, Acceleration, Applications, Instrumentation, Beamline Design, and beam dynamics design codes. Ensuring compatibility across devices and operating systems, it also features integration with Google Docs for collaboration, a code repository (GitHub), a blog platform with comments (WordPress), the potential for ChatGPT integration and interactive graph plotting with Python Plotty to enhance data visualization. This project will maintain public and protected private pages, due to the proprietary nature of the work or research in progress. The public sections will be built to foster dissemination of information and highlight recent work within the NK Labs collaboration, including lectures, published papers, and regular blog posts with open commenting. The private section will support unpublished or nonpublic research, by facilitating collaborative efforts through integrated Google Docs and Python Plotty for shared graphing work. Ultimately, this project strives to make complex scientific knowledge more accessible to the public, foster enhanced collaboration, and serve as a platform for sharing cutting-edge research in Muon Catalyzed Fusion and Accelerators.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Search for the Muon EDM at Muon $g-2$

After 6 years of taking data, the Muon $g-2$ Experiment measured the anomalous magnetic moment of the muon $a_μ$ to a final precision of 127 ppb. In parallel to this analysis, it is possible to perform a measurement of the muon electric dipole moment (EDM) using the straw tracker detectors. In the Standard Model (SM) EDMs are predicted to be vanishingly small. A non-zero muon EDM would constitute physics beyond the SM (BSM) and be a source of charge-parity violation. The current limit on the muon EDM was set at the predecessor experiment at Brookhaven National Laboratory, giving $|d_\mu|<1.8\times10^{-19}\ e\cdot$cm Fermilab aims to improve this by an order of magnitude, which will help to constrain BSM theories. This poster will cover the importance, methodology, and status of this measurement.

Bailey, Lucy [University Coll. London]↗

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 OSTI2018

Muon Borehole Detector Design for Use in 4-D Density Overburden Monitoring

The increase of atmospheric CO2 concentrations has initiated research into carbon sequestration methods. One possibility is to store CO2 in subsurface porous reservoirs. The monitoring of the injected CO2 plume is vital because escaping CO2 poses health and environmental risks. Typically, seismic reflection methods are used to determine the change in density due to the replacement of brine by CO2 in the reservoir, but this is expensive and not continuous. A potential alternative is to use cosmic muon tomography to measure density changes in the reservoir as a function of time. This paper describes the development of a muon detector that will be capable of being deployed in boreholes. The detector has the required dimensions, an angular resolution of approximately 2 degrees, and is robust. The design is based on alternating layers of scintillating rods, which can provide 4-D tomographic data to detect small changes in density at depths up to approximately 2 km. Geant4, a Monte Carlo simulation code, is being used to develop models to guide the design of the physical configuration. Preliminary testing and measurements have been performed to validate the simulation predictions and optimize the performance of the system. The simulation and preliminary experimental results are presented here.

Borehole Detector, CO¬2 Sequestration, Geant4, Muo↗

DOE OSTI2019

Muon loss rates from betatron resonances at the Muon g – 2 Storage Ring at Fermilab

The Muon g–2 Experiment at Fermilab (E989) is directed toward measuring the muon magnetic anomaly, a μ = (g–2)/2, with total statistical and systematic errors of 0.14 ppm. Here, this new measurement will serve as strong probe of effects of as yet undiscovered particles beyond the Standard Model (SM), and perhaps validate or disprove other theoretical models beyond the SM. Of special interest is the reduction of muon losses from the storage ring to achieve the precision needed at the Muon g–2 Experiment.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

US Muon Workshop 2021: A road map for a future Muon Facility

The workshop title “US Muon Workshop 2021: A road map for a future Muon Facility” was held virtually on February 1-2, 2021. The workshop aimed to bring together world experts in muon spectroscopy (µSR) and other techniques along with interested stakeholders to evaluate the scientific need to construct a new µSR facility in the United States (US). The more than 200 participants highlighted several key scientific areas for µSR research, including quantum materials, hydrogen chemistry, and battery materials, and how each area could benefit from a new, high flux pulsed muon source. Experts also discussed aspects of the µSR technique, such as low-energy µSR, novel software developments, alongside beam and detector technologies, that could enable revolutionary advances in µSR at a next-generation facility. The workshop concluded with discussion of a concept being developed for a new µSR facility at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (ORNL). That novel design concept was first envisioned by many of the same µSR experts at a workshop held previously at ORNL in 2016. The participants expressed that the current design had the potential to be a world-leading µSR facility, and strongly encouraged the principal investigators to continue their work in order to refine the concept and determine instrument parameters that would enable new scientific opportunities.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Testing the neutrino content of the muon at muon colliders

Collinear emission of W bosons off a high-energy muon induces a large muon-neutrino component among the Parton Distribution Functions (PDFs) of a muon. In this paper we study the phenomenology related to the ν$_{μ}$ PDF at future high-energy muon colliders. We examine total rates and differential distributions of the $ e{\overline{\nu}}_e $ and Wγ production processes, which receive a large, and often dominant, contribution from this PDF, allowing for a detailed experimental study. As a demonstration of the impact the ν$_{μ}$ PDF could have for searches of new physics, we study the charged-current pair production of a couple of heavy states, components of a SU(2)$_{L}$ doublet. In both $ e{\overline{\nu}}_e $ production and charged-current pair production of heavy states, we compare results obtained using PDFs with those of a fixed-order simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

An effective field theory for muon conversion and muon decay-in-orbit

Muon conversion is one of the best probes of charged lepton flavor violation. The experimental limit is soon expected to improve by four orders of magnitude, thus calling for precise predictions of the shape of the signal spectrum. Equally important are precise predictions for muon decay-in-orbit, the main background for muon conversion. While the calculation of electromagnetic corrections to the two processes above the nuclear scale does not involve significant challenges, it becomes substantially more complex below that scale due to multiple scales, bound-state effects and experimental setup. Here, we present a systematic framework that addresses these challenges by resorting to a series of effective field theories. Combining Heavy Quark Effective Theory (HQET), Non-Relativistic QED (NRQED), potential NRQED, Soft-Collinear Effective Theory I and II, and boosted HQET, we derive a factorization theorem and present the renormalization group equations. Our framework allows for the proper calculation of precise predictions for the rates of the two processes, with crucial implications for the upcoming muon conversion searches. We also provide the most accurate prediction of the signal shape for those searches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Probing the muon ( g − 2) anomaly at the LHC in final states with two muons and two taus

The longstanding muon (g - 2) anomaly, as well as some hints of lepton flavor universality violation in B-meson decays, could be signaling new physics beyond the Standard Model (SM). A minimal R-parity-violating supersymmetric framework with light third-generation sfermions (dubbed as ‘RPV3’) provides a compelling solution to these flavor anomalies, while simultaneously addressing other pressing issues of the SM. We propose a new RPV3 scenario for the solution of the muon (g - 2) anomaly, which leads to an interesting LHC signal of $µ$ + $µ$ - $τ$ + $τ$ - final state. We analyze the Run-2 LHC multilepton data to derive stringent constraints on the sneutrino mass and the relevant RPV coupling in this scenario. We then propose dedicated selection strategies to improve the bound even with the existing dataset. We also show that the high-luminosity LHC will completely cover the remaining muon (g - 2)-preferred parameter space, thus providing a robust, independent test of the muon (g - 2) anomaly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Report from: US Muon Workshop 2021: A Road Map for a Future Muon Facility February 1-2, 2021

The workshop titled “US Muon Workshop 2021: A road map for a future Muon Facility” was held virtually on February 1-2, 2021. The workshop aimed to bring together world experts in muon spectroscopy (µSR) and other techniques along with interested stakeholders to evaluate the scientific need to construct a new µSR facility in the United States (US). The more than 200 participants highlighted several key scientific areas for µSR research, including quantum materials, hydrogen chemistry, and battery materials, and how each area could benefit from a new, high flux pulsed muon source. Experts also discussed aspects of the µSR technique, such as low-energy µSR, novel software developments, and beam and detector technologies that could enable revolutionary advances in µSR at a next-generation facility. The workshop concluded with discussion of a concept being developed for a new µSR facility at the Spallation Neutron Source (SNS) of Oak Ridge National Laboratory (ORNL). That novel design concept was first envisioned by many of the same µSR experts at a workshop held previously at ORNL in 2016. The participants expressed that the current design had the potential to be a world-leading µSR facility, and strongly encouraged the principal investigators to continue their work in order to refine the concept and determine instrument parameters that would enable new scientific opportunities

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗