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Analytic Chromaticity Formulas for the Muon g -2 experiment at fermilab

The Muon g-2 Experiment (E989) at Fermilab measured the muon anomalous magnetic moment aμ with unprecedented precision of 127 ppb using a storage ring. The experiment pushed the limits in terms of accuracy and systematic errors. Achieving the 78-ppb total systematic uncertainty required precise beam dynamics modeling and corrections for effects on the measured muon precession frequency. Here, we derived the first analytic aberration formulas up to the second order for the muon g-2 storage ring’s combined-function electrostatic quadrupoles (superimposed magnetic dipole and electric quadrupole fields) using an order-by-order perturbation method. From these, we obtained the exact chromaticity formulas for three ring models of different granularity and validated them against numerical calculations using COSY INFINITY, achieving analytic-numerical agreement to ⁠$\mathscr{O}(10^{-10})$. This work resolved discrepancies between previous approximate derivations and provided essential beam dynamics results for Runs 4-6 analyses. We also calculated nonlinear chromaticities up to ninth order. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous muon g-2 experiment at Brookhaven National Laboratory, with the final result announced in June 2025.

aberrations

Essay: A Path for the Construction of a Muon Collider

Muons are elementary particles and provide cleaner collision events that can explore higher energies compared to composite particles like protons. Muons are also far heavier than their electron cousins, meaning that they emit less synchrotron radiation that effectively limits the energies of circular electron-positron colliders. These characteristics open up the possibility for a muon collider to surpass the direct energy reach of the Large Hadron Collider while achieving unprecedented precision measurements of standard model processes. In this Essay, after briefly summarizing the progress achieved so far, I identify important missing research and development steps and envision a compelling plan to bring a muon collider to reality in the next two decades. A muon collider could allow for the exploration of physics that is not available with current technologies. For example, it may provide a way to study the Higgs boson directly or probe new particles, including those related to dark matter or other phenomena beyond the standard model. . Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

EFT approach to the endpoint of muon decay-in-orbit

As upcoming experiments aim to probe muon conversion with unprecedented precision, equally precise theoretical predictions are crucial to maximize discovery potential. This applies not only to the new physics signal, muon-electron conversion, but also to its only irreducible background, muon decay-in-orbit (DIO) near the endpoint. Accurate computation of higher-order corrections in bound states is a long-standing challenge due to the difficulty of systematically organizing contributions. In previous work, we developed an Effective Field Theory framework to address this issue and applied it to muon conversion. Here, we extend this approach to the DIO endpoint, a more complex problem due to the presence of a neutrino-antineutrino pair in the final state. We present the most precise prediction to date of the background spectrum relevant for future muon conversion searches, achieving next-to-leading logarithmic prime accuracy for QED corrections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Measurement of three-dimensional inclusive muon-neutrino charged-current cross sections on argon with the MicroBooNE detector

We report the measurement of the triple-differential cross section d 3 σ/dE vis d cos(θ μ )dP μ for inclusive muon-neutrino charged-current scattering on argon. This measurement utilizes data from 6.4 x 10 20 protons on target of exposure collected using the MicroBooNE liquid argon time projection chamber located along the Fermilab Booster Neutrino Beam with a mean neutrino energy of approximately 0.8 GeV. The mapping from reconstructed kinematics to truth quantities is validated within uncertainties by comparing the distribution of reconstructed hadronic energy in data to that of the model prediction in different muon scattering angle bins after applying a conditional constraint from the muon momentum distribution in data. The success of this validation provides confidence that the energy transfer in the MicroBooNE detector is well-modeled within simulation uncertainties, enabling a reliable unfolding to a triple-differential cross section defined at the nominal neutrino flux over muon momentum, muon scattering angle, and visible neutrino energy. This validation not only supports accurate cross-section extraction, but also establishes a critical foundation for tuning interaction models used in future neutrino oscillation measurements. The unfolded measurement covers an extensive phase space, providing a wealth of information useful for future liquid argon time projection chamber experiments measuring neutrino oscillations. Comparisons against a number of commonly used model predictions are included and their performance in different parts of the available phase-space is discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Laser based 100 GeV electron acceleration scheme for muon production

High energy muons, due to their unique ability to penetrate deeply into matter, can enable radiography of structures that cannot be probed by other forms of radiation. Current terrestrial sources of muons require conventional GeV-TeV particle accelerators which are hundreds to thousands of meters in size. Laser wakefield acceleration (LWFA) can achieve acceleration gradients of two-to-three orders of magnitude greater than conventional accelerators, thus shrinking the accelerator to a number of meters. We propose a concept for a compact muon source based on the first self-consistent PIC simulations of an all optical LWFA that uses a guiding channel to achieve electron energies of 100 GeV in a distance of 6 m with a driving laser energy of 300 J in a single stage. From the resulting electron energy spectrum we estimate muon production for this source. We show that this accelerator, coupled with high average power laser driver technology, provides the basis for a high energy and high flux muon source.

laser-produced plasmas

Study of the muon component in the core-corona model using CONEX 3D

The discrepancy between models and data regarding the muon content in air showers generated by ultra-high energy cosmic rays still needs to be solved. The CONEX simulation framework provides a flexible tool to assess the impact of different interaction properties and thus address the muon puzzle. In this work, we present the multidimensional extension of CONEX and show its performance compared to CORSIKA by discussing muon-related air-shower features for three experiments: KASCADE, IceTop, and the Pierre Auger Observatory. We also implement an effective version of the core-corona model to demonstrate the impact of the core effect, as observed at the LHC, on the muon content in air showers produced by ultra-high energy cosmic rays. At a primary energy of E$_{0}$ = 10$^{19}$ eV, we obtain an increase of 15% to 20% in the muon content.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Measuring the muon content of inclined air showers using AERA and the water-Cherenkov detectors of the Pierre Auger Observatory

We present a novel approach for assessing the muon content of air showers with large zenith angles on a combined analysis of their radio emission and particle footprint. We use the radiation energy reconstructed by the Auger engineering radio array (AERA) as an energy estimator and determine the muon number independently with the water-Cherenkov detector array of the Pierre Auger Observatory, deployed on a 1500 m grid. We focus our analysis on air showers with primary energy above 4 EeV to ensure full detection efficiency. Over approximately ten years of accumulated data, we identify a set of 40 high-quality events that are used in the analysis. The estimated muon contents in data are compatible with those for iron primaries as predicted by current-generation hadronic interaction models. This result can be interpreted as a deficit of muons in simulations as a lighter mass composition has been established from X max measurements. This muon deficit was already observed in previous analyses of the Auger Collaboration and is confirmed using hybrid events that include radio measurements for the first time.

Abdul Halim, A. [Adelaide U.]

Explanation of the seasonal variation of cosmic multiple muon events observed with the NOvA Near Detector

The flux of cosmic ray muons at the Earth’s surface exhibits seasonal variations due to changes in the temperature of the atmosphere affecting the production and decay of mesons in the upper atmosphere. Using 1473 live days of data collected by the NuMI Off-axis 𝜈 𝑒 Appearance (NOvA) Near Detector during 2018–2022, we studied the seasonal pattern in the multiple-muon event rate. The data confirm an anticorrelation between the multiple-muon event rate and effective atmospheric temperature, consistent across all the years of data. Previous analyses from MINOS and NOvA saw a similar anticorrelation but did not include an explanation. We find that this anticorrelation is driven by altitude–geometry effects as the average muon production height changes with the season. This has been studied with a CORSIKA cosmic ray simulation package by varying atmospheric parameters, and provides an explanation to a longstanding discrepancy between the seasonal phases of single and multiple-muon events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Muon-induced baryon number violation

The search for charged-lepton flavor violation in muon capture on nuclei is a powerful probe of heavy new physics. A smoking gun signal for μ → e conversion is a monochromatic electron with energy almost equal to the muon mass. We show that light new physics can mimic this signature and that it can also lead to electrons above the μ → e signal peak. A concrete example of such light new physics is μ − -nucleon annihilation into a light dark sector, which can produce an energetic e − as well as e + e − by-products. Due to the size of the muon mass, the exotic muon capture process can be kinematically allowed, while the otherwise stringent constraints, e.g., from proton decay, are kinematically forbidden. We also discuss other relevant constraints, including those from the stability of nuclei and muon capture in the interior of neutron stars. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Reconstruction of cosmic-ray muon events with CUORE

We report the in-situ 3D reconstruction of through-going muons in the CUORE experiment, a cryogenic calorimeter array searching for neutrinoless double beta (0vββ) decay, leveraging the segmentation of the detector. Due to the slow time response of the detector, time-of-flight estimation is not feasible. Therefore, the track reconstruction is performed using a multi-objective optimization algorithm that relies on geometrical information from the detector as a whole. We measure the integral flux of cosmic-ray muons underground at the Laboratori Nazionali del Gran Sasso, and find our value to be in good agreement with other experiments that have performed a similar measurement. To our knowledge, this work represents the first demonstration of 3D particle tracking and reconstruction of through-going muons with per-event angular determination in a millikelvin cryogenic detector array. The analysis performed for this work will be critical for validating the muon-related background in CUPID, a next-generation 0vββ experiment, and for follow-up studies on detector response and on delayed products induced by cosmic-ray muons.

Adams, D. Q. [University of South Carolina]

Beam Design for Muon Catalyzed Fusion

Fusion holds great promise as a clean and abundant energy source. However, traditional thermonuclear fusion encounters significant challenges due to the extreme temperatures required to overcome the coulomb barrier for two nuclei to fuse. In contrast, muon-catalyzed fusion presents an alternative approach that can surmount this barrier at significantly lower temperatures. Muons, with properties resembling those of electrons but 200 times heavier, can effectively reduce the atomic orbital radius, enabling central nuclei to overcome the coulomb force through the strong force. By introducing muons into a mixture of deuterium and tritium (two hydrogen isotopes), fusion is facilitated, releasing a 3.5MeV alpha particle and a 14.1MeV neutron. In the majority of cases, the muon is liberated and can initiate further fusions. However, approximately 0.8% of the time, it adheres to the alpha particle and remains bound until it either decays or undergoes reactivation through collisio nal ionization. To maximize the number of fusions per muon, it is crucial to enhance the cycling rate and reactivation fraction. Theoretical predictions and experimental data both suggest that the sticking rate decreases with increasing density. However, there exists a discrepancy between experimental observations and theoretical estimations regarding the extent of this decrease. To address these disparities, this experiment aims to investigate the cycling rate and sticking fraction under higher temperatures and pressures than previously explored.

43 PARTICLE ACCELERATORS

Muon Flux Variance from Severe Atmospheric Conditions

We analyze data from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the QuarkNet Research Group at Fermilab to study the variance in muon flux due to extreme weather conditions. We considered three high-intensity storms for each season: winter, spring, and summer. The most significant observation was during winter, with a ~125% increase in muon flux corresponding to a temperature drop of ~20K. Additionally, we are developing CosmicWatch muon detectors to be used in tests for the MMBC/MAMBA Bubble Chamber. A pair of these detectors will be employed to trigger on muons, providing extremely precise and inexpensive tracking granularity in the form of a muon telescope.

Aamir, Yusuf

Multi-Differential Semi-Inclusive Charged-Current Muon Neutrino Cross Sections on Helium-4 in MINERvA and the Helium-to-CH Target Cross Section Ratio

A comprehensive international effort has been underway to elucidate the properties and behaviors of neutrinos. A major source of systematic uncertainties in studying neutrino-induced interactions comes from neutrino-nucleus cross-section models, highlighting the need for more precise statistical measurements. MINERvA, an on-axis neutrino-nucleus scattering experiment located at the Fermi National Accelerator Laboratory, was established to produce neutrino cross-section measurements with many different nuclei. The helium target is the lightest nucleus to be measured by MINERvA. Using the NuMI medium energy muon neutrino data set, we present preliminary results and summarize the extraction of the charged current (CC) muon neutrino - helium-4 semi-inclusive ($\nu_{\mu}$+$^{4}\textrm{He}$$\rightarrow$$\mu^{-}$+N$\pi$+M$\textit{p}$) multi-differential cross-section extraction as a function of transverse ($P_{T}$) and longitudinal ($P_{L}$) muon momentum with respect to the neutrino beamline. We define the final state topology as CC-N$\pi$M$\textit{p}$, with at least two reconstructed tracks: a muon and a combination of N protons and M pions, where $N + M > 0$. To probe the dependence on the size of the nucleus in neutrino-induced interaction phenomena we present a differential cross-section ratio of helium-4 to MINERvA's hydrocarbon target (\textrm{CH}) as a function of transverse muon momentum.

Nguyen, Christian

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

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

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

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.

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.