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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Beam Dynamics of the Muon $g\textrm{-}2$ Experiment

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of 0.20 ppm. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: \texttt{gm2ringsim} (an internal Geant4-based code), \textit{COSY INFINITY}, and \textit{BMAD}. The advantages of \texttt{gm2ringsim} include using CAD-based geometry and modelling the detector effects. \textit{COSY INFINITY} is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

The Case for a Muon Collider

In the search for future high-energy collider technologies, the muon collider has emerged as an extremely promising long-term option. The muon’s large mass relative to the electron allows it to reach high mass energies with a small footprint. This talk will first provide an overview of the scientific potential of a future muon collider, followed by a discussion of the key technical challenges that must be overcome, given the muon’s short lifetime and the many acceleration stages in a collider. This talk concludes with encouragement for audiences to join the ongoing international research and development efforts for a muon collider.

Keeler, Dominic [Purdue U., West Lafayette] (ORCID↗
DOE OSTI2025

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

The Muon $g-2$ Experiment at Fermilab aims to measure the muon magnetic moment anomaly, $a_{\mu} = (g-2)/2$, with a final accuracy of 0.14 parts per million (ppm). A $3.1$-GeV muon beam is injected into a storage ring of $14\,$m diameter, in the presence of a $1.45\,$T magnetic field. The anomaly $a_\mu$ can be extracted by accurately measuring the anomalous muon spin precession frequency $\omega_a$, based on the arrival time distribution of decay positrons observed by $24$ calorimeters, and the magnetic field. In 2023, the experiment published its second result based on the two datasets Run-2 and Run-3, reaching the unprecedented sensitivity of $0.21\,$ppm --- a factor $\sim2.2$ improvement since its first result published in 2021, based on the first dataset (Run-1). In this paper, we will focus on the measurement of the $\omega_a$ frequency, describing the techniques and major sources of systematic uncertainty in the 2023 publication, and outlining the improvements since the 2021 result. We will also cover the status of the ongoing $\omega_a$ analysis for the last three datasets, collected from 2020 to 2023, along with the projected uncertainties on the final Muon $g-2$ measurement at Fermilab.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

The composition of cosmic rays near the Bend (10 to the 15th power eV) from a study of muons in air showers at sea level

The distribution of muons near shower cores was studied at sea level at Fermilab using the E594 neutrino detector to sample the muon with E testing 3 GeV. These data are compared with detailed Monte Carlo simulations to derive conclusions about the composition of cosmic rays near the bend in the all particle spectrum. Monte Carlo simulations generating extensive air showers (EAS) with primary energy in excess of 50 TeV are described. Each shower record contains details of the electron lateral distribution and the muon and hadron lateral distributions as a function of energy, at the observation level of 100g/cm. The number of detected electrons and muons in each case was determined by a Poisson fluctuation of the number incident. The resultant predicted distribution of muons, electrons, the rate events are compared to those observed. Preliminary results on the rate favor a heavy primary dominated cosmic ray spectrum in energy range 50 to 1000 TeV.

Goodman, J. A.↗
NASA NTRS1985

Muon and neutrino results from KGF experiment at a depth of 7000 hg/square cm

The KGF nucleon decay experiment at a depth of 7000 hg/sq cm has provided valuable data on muons and neutrinos. The detector comprised of 34 crossed layers of proportional counters (cross section 10 x 10 sq cm; lengths 4m and 6m) sandwiched between 1.2 cm thick iron plates can record tracks of charged particles to an accuracy of 1 deg from tracks that traverse the whole of the detector. A special two-fold coincidence system enables the detector to record charged particles that enter at very large zenith angles. In a live time of 3.6 years about 2600 events have been recorded. These events include atmospheric muons, neutrino induced muons from rock, stopping muons, showers and events which have their production vertex inside the detectors. The results on atmospheric muons and neutrino events are presented.

Krishnaswamy, M. R.↗
NASA NTRS1985

Measurement of muon intensity by Cerenkov method

Optical detection is an important technique in studies and observations of air showers, muons and relevant phenomena. The muon intensity is measured in a proper energy range and to study some problems about Cerenkov radiation of cosmic rays are studied, by a muon-telescope operated with Cerenkov detector. It is found that the measured muon intensity agrees with the integral energy spectrum of cosmic ray muons.

Liu, Z. H.↗
NASA NTRS1985

Results of investigation of muon fluxes of superhigh energy cosmic rays with X-ray emulsion chambers

The overall data from the investigation of the cosmic ray muon flux in the range of zenith angles (0-90) deg within the energy range (3.5 to 5.0) TeV is presented. The exposure of large X-ray emulsion chambers underground was 1200 tons. year. The data were processe using the method which was applied in the experiment Pamir and differred from the earlier applied one. The obtained value of a slope power index of the differential energy spectrum of the global muon flux is =3.7 that corresponds to the slope of the pion generation differential spectrum, gamma sub PI = 2.75 + or - .04. The analysis of the muon zenith-angular distribution showed that the contribution of rapid generation muons in the total muon flux agree the best with the value .2% and less with .7% at a 90% reliability level.

Ivanenko, I. P.↗
NASA NTRS1988

Muon motion in titanium hydride

Motional narrowing of the transverse-field muon spin rotation signal was observed in gamma-TiH(x) for x = 1.83, 1.97, and 1.99. An analysis of the data for TiH1.99 near room temperature indicates that the mechanism responsible for the motion of the muon out of the octahedral site is thermally activated diffusion with an attempt frequency comparable to the optical vibrations of the lattice. Monte Carlo calculations to simulate the effect of muon and proton motion upon the muon field-correlation time were used to interpret the motional narrowing in TiH1.97 near 500 K. The interpretation is dependent upon whether the Bloembergen, Purcell, and Pound (BPP) theory or an independent spin-pair relaxation model is used to obtain the vacancy jump rate from proton NMR T1 measurements. Use of BPP theory shows that the field-correction time can be obtained if the rate of motion of the muon with respect to the rate of the motion for the protons is decreased. An independent spin-pair relaxation model indicates that the field-correlation time can be obtained if the rate of motion for the nearest-neighbor protons is decreased.

Kempton, J. R.↗
DOE OSTI2024

Implementation of a Time-domain Cosmic-ray-muon Tagger for the NEXUS Low-background Cryogenic Facility

Quantifying the effects of radiation on the operation of qubits both as quantum information systems as well as particle detectors has emerged as a pressing issue in quantum science in recent years. We present an overview of the design, operation, and deployment of a 90-$\mathrm{in}^2$ three-panel muon detector for use in the NEXUS experimental facility at Fermilab to temporally isolate correlated errors in qubits and determine if they possess an astrophysical origin. Constructed with three scintillator-attached PMTs read out with NIM modules in a triply-coincident logic scheme, we measure a surface-level muon luminosity of 9.7425 muons per second---consistent with an average surface-level cosmic-ray flux of approximately one muon per square centimeter per minute. Integrating the NIM modules with an MCC 128 DAQ HAT and Raspberry Pi, a Python script records exactly when a muon struck the detector and writes a timestamp to a log file for follow-up cross referencing. This experiment will broadly contribute to further studies aimed at understanding the source and mitigation of information loss in qubits.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

An improved direct limit on the muon electric dipole moment

A limit on the permanent electric dipole moment (EDM) of the positive muon is presented based on data from the Fermilab Muon g-2 Experiment taken between 2019 and 2020. The tracking detectors measure the average vertical decay angle of positrons from muon decays, enabling a search for an interaction between a possible muon EDM $d_μ$ and the lab-frame magnetic field. The result, $d_μ= (-0.35 \pm 0.19_{\mathrm{stat}} \pm 0.34_{\mathrm{sys}}) \times10^{-19}~e\cdot$cm, is consistent with zero and sets a new direct limit on the muon EDM of $|d_μ|<1.10\times10^{-19}~e\cdot$cm at the 95 percent confidence level.

Aguillard, D. P. [Michigan U.] (ORCID:000000025556↗
DOE OSTI2026

Multiple Coulomb scattering for muon energy reconstruction in SBND Monte Carlo simulations

The Short Baseline Near Detector (SBND) is a liquid argon time projection chamber (LArTPC) located 110 meters downstream of the Booster Neutrino Beam target at Fermilab \cite{SBN}. The LArTPC is a detector technology with unprecedented position and calorimetric resolution for precise neutrino studies. The most dominant neutrino interaction topology in SBND is charged-current quasi-elastic muon neutrino-argon interactions, where the final state consists of a muon and a proton. Here, muons often travel long distances, sometimes exiting the detector before stopping. This loss of information creates a challenge for accurate energy estimation. There have been efforts in the MicroBooNE and ICARUS collaborations to improve energy estimation using a phenomenon known as Multiple Coulomb Scattering (MCS), which describes the jagged path taken by muons through a detector due to continuous Coulomb interactions with argon atoms. Building on these efforts, my project aims to improve an MCS-based approach to estimating the energies of exiting muons in SBND.

Puig, Xilonem Angeles [Mt. Holyoke Coll.; Fermilab↗
DOE OSTI2025

The fixed probe storage ring magnetometer for the Muon g-2 experiment at Fermi National Accelerator Laboratory

The goal of the FNAL E989 experiment is to measure the muon magnetic anomaly to unprecedented accuracy and precision at the Fermi National Accelerator Laboratory. To meet this goal, the time and space averaged magnetic environment in the muon storage volume must be known to better than 70 ppb. A new pulsed proton nuclear magnetic resonance (NMR) magnetometer was designed and built at the University of Washington, Seattle to track the temporal stability of the 1.45 T magnetic field in the muon storage ring at this precision. It consists of an array of 378 petroleum jelly based NMR probes that are embedded in the walls of muon storage ring vacuum chambers and custom electronics built with readily available modular radio frequency (RF) components. We give NMR probe construction details and describe the functions of the custom electronic subsystems. The excellent performance metrics of the magnetometer are discussed, where after 8 years of operation the median single shot resolution of the array of probes remains at 650 ppb.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Measurement of the positive muon anomalous magnetic moment to 127 ppb

A new measurement of the magnetic anomaly $a_μ$ of the positive muon is presented based on data taken from 2020 to 2023 by the Muon $g-2$ Experiment at Fermi National Accelerator Laboratory (FNAL). This dataset contains over 2.5 times the total statistics of our previous results. From the ratio of the precession frequencies for muons and protons in our storage ring magnetic field, together with precisely known ratios of fundamental constants, we determine $a_μ = 116\,592\,0710(162) \times 10^{-12}$ (139 ppb) for the new datasets, and $a_μ = 116\,592\,0705(148) \times 10^{-12}$ (127 ppb) when combined with our previous results. The new experimental world average, dominated by the measurements at FNAL, is $a_μ(\text{exp}) =116\,592\,0715(145) \times 10^{-12}$ (124 ppb). The measurements at FNAL have improved the precision on the world average by over a factor of four.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Electroweak observables in neutrino-electron scattering from a muon storage ring

We investigate the sensitivity of a companion neutrino detector situated in the plane of a high-energy, high-intensity muon storage ring to elastic ν μ and ν e scattering on electrons (EνES). Assuming a muon collider with center-of-mass energies of up to 10 TeV, we report sensitivity to the weak couplings g V and g A up to around 0.05% relative error, and sensitivity to the weak mixing angle in the momentum transfer Q ∈ [10 −2 , 2] GeV range up to around 0.03% relative error. EνES measurements with high-energy muon storage rings allow one to directly interrogate the momentum-transfer regime associated with the NuTeV anomaly. This level of precision allows unique sensitivity to the momentum-dependence of sin 2 θ W . We estimate that with the neutrinos from a E μ = 1.5 TeV (or higher) muon collider, the hypothesis that sin 2 θ W does not “run” can be safely ruled out.

electroweak precision physics↗
DOE OSTI2025

Searching for neutrino self-interactions at future muon colliders

Multi-TeV muon colliders offer a powerful means of accessing new physics coupled to muons while generating clean and intense high-energy neutrino beams via muon decays. We study a fixed-target experiment leveraging the neutrino beams and a forward detector pointing at the interaction point of the muon collider. The sensitivity to neutrino self-interactions is analyzed as a feasibility study, focusing on the leptonic scalar ϕ exclusively coupled to the Standard Model neutrinos. Our work shows that projections from both the main and forward detectors can enhance the existing limits by two orders of magnitude, surpassing other future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Identification of low-momentum muons in the CMS detector using multivariate techniques in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

“Soft” muons with a transverse momentum below 10 GeV are featured in many processes studied by the CMS experiment, such as decays of heavy-flavor hadrons or rare tau lepton decays. Maximizing the selection efficiency for these muons, while simultaneously suppressing backgrounds from long-lived light-flavor hadron decays, is therefore important for the success of the CMS physics program. Multivariate techniques have been shown to deliver better muon identification performance than traditional selection techniques. To take full advantage of the large data set currently being collected during Run 3 of the CERN LHC, a new multivariate classifier based on a gradient-boosted decision tree has been developed. It offers a significantly improved separation of signal and background muons compared to a similar classifier used for the analysis of the Run 2 data. The performance of the new classifier is evaluated on a data set collected with the CMS detector in 2022 and 2023, corresponding to an integrated luminosity of 62 fb -1 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Muon capture on Li 6 , C 12 , and O 16 from ab initio nuclear theory

Muon capture on nuclei is one of the most promising probes of the nuclear electroweak current driving the yet-hypothetical neutrinoless double-beta (0νββ) decay. Both processes involve vector and axial-vector currents at finite momentum transfer, q ~ 100 MeV, as well as the induced pseu doscalar and weak-magnetism currents. Comparing measured muon-capture rates with reliable ab initio nuclear-theory predictions could help us validate these currents. To this end, we compute partial muon-capture rates for 6 Li, 12 C and 16 O, feeding the ground and excited states in 6 He, 12 B and 16 N, using ab initio no-core shell model with two- and three-nucleon chiral interactions. Here, we remove the spurious center-of-mass motion by introducing translationally invariant operators and approximate the effect of hadronic two-body currents by Fermi-gas model. We solve the bound-muon wave function from the Dirac wave equations in the Coulomb field created by a finite nucleus. We find that the computed rates to the low-lying states in the final nuclei are in good agreement with the measured counterparts. We highlight sensitivity of some of the transitions to the sub-leading three-nucleon interaction terms. We also compare summed rates to several tens of final states with the measured total capture rates and note that we slightly underestimate the total rate with this simple approach due to limited range of excitation energies

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Searching for heavy neutral leptons at a future muon collider

As the planning stages for a high energy muon collider enter a more concrete era, an important question arises as to what new physics could be uncovered. A TeV-scale muon collider is also a vector boson fusion (VBF) factory with a very clean background, and as such it is a promising environment to look for new physics that couples to the electroweak (EW) sector. In this paper, we explore the ability of a future TeV-scale muon collider to search for Majorana and Dirac heavy neutral leptons (HNLs) produced via EW bosons. Employing a model-independent, conservative approach, we present an estimation of the production and decay rate of HNLs over a mass range between 200 GeV and 9.5 TeV in two benchmark collider proposals with s = 3 , 10 TeV, as well as an estimation of the dominant Standard Model (SM) background. We find that exclusion limits for the mixing between the HNLs and SM neutrinos can be as low as O ( 10 − 6 ) . Additionally, we demonstrate that a TeV-scale muon collider allows for the ability to discriminate between Majorana and Dirac type HNLs for a large range of mixing values. Published by the American Physical Society 2024

Kwok, Tsz Hong↗