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Mass measurement of 27 P to constrain type-I x-ray burst models and validate the isobaric multiplet mass equation for the $A = 27, T = \frac{3}{2}$ isospin quartet

Background: Light curves are the primary observable of type-I x-ray bursts. Computational x-ray burst models must match simulations to observed light curves. Most of the error in simulated curves comes from uncertainties in rp process reaction rates, which can be reduced via precision mass measurements of neutron-deficient isotopes in the rp process path. Purpose: Perform a precise atomic mass measurement of 27 P. Use this new measurement to calculate rp process reaction rates and input these rates into an x-ray burst model to reduce simulated light curve uncertainty. Use the mass measurement of 27 P to validate the isobaric multiplet mass equation (IMME) for the A = 27 T = 3/2 isospin quartet which 27 P belongs to. Method: High-precision Penning trap mass spectrometry utilizing the time-of-flight ion cyclotron resonance technique was used to determine the atomic mass of 27 P. The MESA code (Modules for Experiments in Stellar Astrophysics) was then used to simulate x-ray bursts using a one-dimensional multizone model to produce updated light curves. Results: The mass excess of 27 P was measured to be –670.7(6) keV, a 14-fold precision increase over the mass reported in the 2020 Atomic Mass Evaluation (AME2020). The 26 Si(p, $γ$) 27 P– 27 P($γ$, p) 26 Si rate equilibrium has been determined to a higher precision based on the precision mass measurement of 27 P. x-ray burst light curves were produced with the MESA code using the new reaction rates. Changes in the mass of 27 P seem to have minimal effect on light curves, even in burster systems tailored to maximize impact. Conclusion: The mass of 27 P does not play a significant role in x-ray burst light curves. It is important to understand that more advanced models do not just provide more precise results, but often qualitatively different ones. This result brings us a step closer to being able to extract stellar parameters from individual x-ray burst observations. In addition, the IMME has been validated for the A = 27, T = 3/2 quartet. The normal quadratic form of the IMME using the latest data yields a reduced $χ$ 2 of 2.9. Finally, the cubic term required to generate an exact fit to the latest data matches theoretical attempts to predict this term.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Capability at ORNL: High Precision Uranium Titration

Destructive analytical measurements establish a nuclear facility’s nuclear material inventory and inventory differences for Nuclear Material Accountancy and Control. A nuclear laboratory’s ability to perform accurate high-precision analytical measurements is key for tracking large inventories within a facility’s material balance areas and during production to track material movement through dynamic processes. For uranium, these measurements are made by using several established high-precision measurement protocols. These include isotope dilution mass spectrometry, gravimetry, and potentiometric titrations. Whatever measurement technique a nuclear lab chooses to use, reference materials (RMs) with certified attributes and accompanying uncertainties are used to calibrate measurement systems, and are the cornerstone for accurate results. In addition to calibration, RMs provide for metrological traceability, are used for method development and validation, and thus provide critical evaluations of the appropriateness and performance of analytical processes used. Evaluations may include validation that a method is fit-for-purpose, quantification of systematic and random biases, and the evaluation of long-term and short-term performance metrics. High-precision measurement techniques require that measured attributes be certified to a high degree of precision in the RMs used—ultimately, to a higher degree than that of the measurement technique itself. The US authority on the production of special nuclear material Certified Reference Materials is the NBL Program Office (NBLPO), formally known as New Brunswick Laboratory (NBL). The NBLPO is responsible for the sales and distribution of existing NBL certified reference materials (CRMs) and for the production of the next generation of nuclear RMs. To accomplish its mission, NBLPO is establishing key base capabilities within the DOE laboratory complex that formerly existed at the NBL laboratory. The Nuclear Analytical Chemistry (NAC) section within the Chemical Sciences Division (CSD) at Oak Ridge National Laboratory (ORNL) is currently working with NBLPO to set up laboratory and measurement capabilities to provide measurements and capabilities for production and/or recertification of existing and future CRMs for uranium assay. The NBL-developed high-precision titration (HPT) method is a critically-evaluated, extremely precise and accurate primary method utilized for the determination of uranium content in a variety of uranium materials. The HPT method, combined with detailed balance weighing protocols, provides for an analytical methodology that is unsurpassed in precision and one in which all sources of error have been evaluated, a requirement of CRM certification. HPT capability within the United States was lost with the closure of the labs at NBL. The NAC has been collaborating with NBLPO to stand up and demonstrate the capability to perform uranium assay via HPT at ORNL. HPT can produce results with an expanded uncertainty of approximately 0.01% for pure uranium compounds, with typical precisions of <0.006%. The major tasks required to stand up the method at ORNL were the refurbishment of a dedicated lab and equipment setup, procedure development, analyst training, establishing method-specific quality assurance, and qualification of an analyst to perform the method. This report summarizes these tasks, outlines the documents drafted, and gives the outcome of the qualification titrations.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Precise β branching-ratio measurement for the 0 + → 0 + superallowed decay of 34 Ar

We have measured the branching ratio for the superallowed 0 + → 0 + β transition from 34 Ar to be 0.9448(8), and determined its ft value to be 3058.1(28) s, a result with ±0.09% precision, which is a factor of three improvement over the previous result based on current world data. The ft-value ratio for the mirror pair of superallowed transitions 34 Ar → 34 Cl and 34 Cl → 34 S, becomes the most precise yet measured and, in a sensitive test of the method used to calculate the isospin-symmetry-breaking correction, δ C , it agrees well with the ratio as calculated with Woods-Saxon radial wave functions. This confirms the method used in the most recent survey of superallowed decays to extract V ud , the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. Additionally, our branching-ratio results for the four observed Gamow-Teller branches to 1 + states in 34 Cl are shown to agree well with shell-model calculations based on the same effective interactions that were used in the determination of δ C .

39 ≤ A ≤ 58↗

Dark Energy Survey: A 2.1% measurement of the angular baryonic acoustic oscillation scale at redshift z eff = 0.85 from the final dataset

Here, we present the angular diameter distance measurement obtained with the baryonic acoustic oscillation (BAO) feature from galaxy clustering in the completed Dark Energy Survey, consisting of six years (Y6) of observations. We use the Y6 BAO galaxy sample, optimized for BAO science in the redshift range 0.6 < z <1.2, with an effective redshift at z eff = 0.85 and split into six tomographic bins. The sample has nearly 16 million galaxies over 4,273 square degrees. Our consensus measurement constrains the ratio of the angular distance to sound horizon scale to D M ⁡(z eff )/r d = 19.51 ± 0.41 (at 68.3% confidence interval), resulting from comparing the BAO position in our data to that predicted by planck Λ⁢CDM via the BAO shift parameter α =(D M /r d )/(D M /r d ) PLANCK . To achieve this, the BAO shift is measured with three different methods, angular correlation function (ACF), angular power spectrum (APS), and projected correlation function (PCF), obtaining α = 0.952 ± 0.023, 0.962 ± 0.022, and 0.955 ± 0.020, respectively, which we combine to α = 0.957 ± 0.020, including systematic errors. When compared with the Λ⁢CDM model that best fits planck data, this measurement is found to be 4.3% and 2.1⁢σ below the angular BAO scale predicted. To date, it represents the most precise angular BAO measurement at z > 0.75 from any survey and the most precise measurement at any redshift from photometric surveys. The analysis was performed blinded to the BAO position, and it is shown to be robust against analysis choices, data removal, redshift calibrations, and observational systematics.

79 ASTRONOMY AND ASTROPHYSICS↗

“Unification” of BSM searches and SM measurements: the case of lepton+E T and m W

We develop the idea that the unprecedented precision in Standard Model (SM) measurements, with further improvement at the HL-LHC, enables new searches for physics Beyond the Standard Model (BSM). As an illustration, we demonstrate that the measured kinematic distributions of the ℓ + E T final state not only determine the mass of the W boson, but are also sensitive to light new physics. Such a search for new physics thus requires a simultaneous fit to the BSM and SM parameters, “unifying” searches and measurements at the LHC and Tevatron. In this paper, we complete the program initiated in our earlier work [1]. In particular, we analyze (i) novel decay modes of the W boson with a neutrinophilic invisible scalar or with a heavy neutrino; (ii) modified production of W bosons, namely, associated with a hadrophilic invisible Z′ gauge boson; and (iii) scenarios without an on-shell W boson, such as slepton-sneutrino production in the Minimal Supersymmetric Standard Model (MSSM). Here, we complement our previous MSSM analysis in [1] by considering a different kinematic region. Our results highlight that new physics can still be directly discovered at the LHC, including light new physics, via SM precision measurements. Furthermore, we illustrate that such BSM signals are subtle, yet potentially large enough to affect the precision measurements of SM parameters themselves, such as the W boson mass.

Electroweak Precision Physics↗

Measurement of C P Violation in B 0 → ψ ( → ℓ + ℓ − ) K S 0 ( → π + π − ) Decays

A measurement of time-dependent C P violation in the decays of B 0 and B ¯ 0 mesons to the final states J / ψ ( → μ + μ − ) K S 0 , ψ ( 2 S ) ( → μ + μ − ) K S 0 and J / ψ ( → e + e − ) K S 0 with K S 0 → π + π − is presented. The data correspond to an integrated luminosity of 6 fb − 1 collected at a center-of-mass energy of s = 13 TeV with the LHCb detector. The C P -violation parameters are measured to be S ψ K S 0 = 0.717 ± 0.013 ( stat ) ± 0.008 ( syst ) and C ψ K S 0 = 0.008 ± 0.012 ( stat ) ± 0.003 ( syst ) . This measurement of S ψ K S 0 represents the most precise single measurement of the CKM angle β to date and is more precise than the current world average. In addition, measurements of the C P -violation parameters of the individual channels are reported and a combination with the LHCb Run 1 measurements is performed. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Aaij, R. (ORCID:0000000305331952)↗

Solar data uncertainty impacts on MCMC methods for r-process nucleosynthesis

In recent work, we developed a Markov Chain Monte Carlo (MCMC) procedure to predict the ground state masses capable of forming the observed Solar r-process rare-earth abundance peak. By applying this method to nucleosynthesis calculations which make use of distinct astrophysical conditions and comparing our results to the latest precision mass measurements, we are able to shed light on the conditions/masses capable of producing a rare-earth peak which matches Solar data. Here we examine how our mass predictions change when using a few different sets of r-process Solar abundance residuals that have been reported in the literature. We explore how the differing error estimates of these Solar evaluations propagate through the Markov Chain Monte Carlo to our mass predictions. We find that Solar data which reports the rare-earth peak to have its highest abundance at mass number A = 162 can require distinctly different mass predictions from data with the peak centered at A = 164. Nevertheless, we find that two important general conclusions from past work, regarding the inconsistency of ‘cold’ astrophysical outflows with current mass measurements and the need for local stability at N = 104 in ‘hot’ scenarios, remain robust in the face of differing Solar data evaluations. Additionally, we show that the masses our procedure finds capable of producing a peak at A < 164 are not in line with the latest precision mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Measurement of Neutron Multiplicity in Charged Current Neutrino Interactions on Oxygen

The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a 26-ton gadolinium-doped water Cherenkov detector located 100~meters downstream in the Booster Neutrino Beam (BNB) at the Fermi National Accelerator Laboratory (Fermilab). Its primary goals are to (1) measure the neutron yield from $\nu_\mu$ interactions as a function of momentum transfer $Q^2$ so that neutrino-nucleus interaction models can be better constrained, and (2) demonstrate the power of novel, fast-timing detectors with the first deployment of Large Area Picosecond PhotoDetectors (LAPPDs). Current knowledge of neutrino-nucleus interactions fall short in modeling the topologies of such interactions, leading to inaccurate reconstruction of event kinematics such as particle energy, direction, and vertex. As a consequence, the accuracy of cross section measurements is impacted, which is necessary for precise physics measurements. Neutrons are an indication of inelasticity and affect the determination of the energy of the parent neutrino. Quantifying the neutron yield is a step towards reducing the associated uncertainties, and thus improving our understanding of these complex interactions and benefiting the next generation of long-baseline neutrino experiments. ANNIE will make use of LAPPDs to measure neutron multiplicity of CC-0$\pi$ $\nu_\mu$ interactions on oxygen, making it the first experiment to deploy an array of these photodetectors. Because the LAPPD is a novel photodetection technology, much customization is required to integrate it into existing electronics. The first half of this thesis covers the significant progress made towards the first deployment of the LAPPD system. From its test stand at Fermilab, the LAPPD system was systematically tested and put together until deployment readiness was achieved. I present my contributions to the design, fabrication, and testing of the waterproof housing and cables, and the commissioning of the LVHV board that powers the LAPPD and its readout electronics. These efforts brought the LAPPD system significantly closer to deployment, and eventually first data. The second half of this thesis presents the vertex and energy reconstruction algorithms developed to analysis the beam data with PMT-only information. While much progress has been made towards the deployment of LAPPDs, with several in the detector tank, efforts to integrate the LAPPD datastream are in progress. Thus, I developed a ring edge detection technique using PMT data to fit the muon vertex and determine its energy. The analysis in this thesis finds average neutron yields of $\Bar{n}_{data} = 0.452 \pm 0.039 (\text{stat}) \pm 0.27 (\text{sys})$ for a selection of muon neutrino candidates in the fiducial volume of ANNIE and corrected with an averaged neutron detection efficiency. An equivalent analysis for simulated beam data results in an average neutron yield of $\Bar{n}_{MC} = 0.582 \pm 0.018 (\text{stat}) \pm 0.25 (\text{sys})$. Future work includes application of efficiency corrections at a positional level, quantification of all systematic uncertainties, and neutron multiplicity measurements with other event topologies.

43 PARTICLE ACCELERATORS↗

Characterization of a modified printed optical particle spectrometer for high-frequency and high-precision laboratory and field measurements

Abstract. The printed optical particle spectrometer (POPS) is a lightweight, low-cost instrument for measurements of aerosol number concentrations and size distributions. This work reports on modifications of the Handix Scientific commercial version of the POPS to facilitate its use in multi-instrument aerosol sampling systems. The flow system is modified by replacing the internal pump with a needle valve and a vacuum pump. The instrument is integrated into closed-flow systems by routing the sheath flow from filtered inlet air. A high-precision multichannel analyzer (MCA) card is added to sample the analog pulse signal. The MCA card is polled at 10 Hz frequency using an external data acquisition system and improves upon the count-rate limitation associated with the POPS internal data acquisition system. The times required to change the concentration between 90 % and 10 % and vice versa for a step change in concentration were measured to be 0.17 and 0.41 s at a flow rate of 5 cm3 s−1. This yields a sampling frequency of ∼ 1–2 Hz, below which the amplitude of measured fluctuations is captured with > 70 % efficiency. The modified POPS was integrated into the dual tandem differential mobility analyzer system to explore the coalescence of dimer particles. Results show that the pulse-height response increases upon dimer coalescence. The magnitude of the increase is broadly consistent with the change in light-scattering amplitude predicted by the T-matrix method. It is anticipated that this modified version of the POPS will extend the utilization of the technique for a range of field and laboratory applications.

54 ENVIRONMENTAL SCIENCES↗

Solar Contamination in Extreme-precision Radial-velocity Measurements: Deleterious Effects and Prospects for Mitigation

Solar contamination, due to moonlight and atmospheric scattering of sunlight, can cause systematic errors in stellar radial velocity (RV) measurements that significantly detract from the ∼10 cm s{sup −1} sensitivity required for the detection and characterization of terrestrial exoplanets in or near habitable zones of Sun-like stars. The addition of low-level spectral contamination at variable effective velocity offsets introduces systematic noise when measuring velocities using classical mask-based or template-based cross-correlation techniques. Here we present simulations estimating the range of RV measurement error induced by uncorrected scattered sunlight contamination. We explore potential correction techniques, using both simultaneous spectrometer sky fibers and broadband imaging via coherent fiber imaging bundles, that could reliably reduce this source of error to below the photon-noise limit of typical stellar observations. We discuss the limitations of these simulations, the underlying assumptions, and mitigation mechanisms. We also present and discuss the components designed and built into the NEID (NN-EXPLORE Exoplanet Investigations with Doppler spectroscopy) precision RV instrument for the WIYN 3.5 m telescope, to serve as an ongoing resource for the community to explore and evaluate correction techniques. We emphasize that while “bright time” has been traditionally adequate for RV science, the goal of 10 cm s{sup −1} precision on the most interesting exoplanetary systems may necessitate access to darker skies for these next-generation instruments.

79 ASTRONOMY AND ASTROPHYSICS↗

Calibration of the DUNE Far Detector Using Cosmic-ray Muon Events

The Deep Underground Neutrino Experiment (DUNE) aims to set new limits on parameters associated with neutrino oscillations, neutrino astrophysics, and beyond the Standard Model (SM) searches such as nucleon decay. DUNE will quantify the magnitude of CP violation in the lepton sector, and determine the neutrino mass ordering. These benefit highly from the large target mass and excellent imaging, tracking, and particle identification capabilities of Liquid Argon Time Projection Chambers (LArTPCs). Detector calibration is essential to make precise physics measurements. For instance, accurate energy reconstruction is necessary for measuring many of the aforementioned quantities with the precision required for discovering new physics and fully exploiting the capabilities of the detector. Cosmic muons are a freely available natural source of calorimetric data and can be used for calibrating various detector parameters. This thesis provides an analysis of simulated cosmic-ray muon events generated with the Muon Simulation Underground (MUSUN) generator in the DUNE horizontal drift (HD) far detector (FD). The study focuses on analysing the energy and angular distribution of various classes of muon events, as well as characterising the different particles produced by cosmic muon interactions. The analysis of π0 → 2γ events within the cosmic-ray muon sample is presented in this thesis with a detailed study of reconstructing electromagnetic showers. The π0 mass is reconstructed within the DUNE FD, yielding a value of (136 ± 7) MeV/c2. Additionally, the thesis introduces methods for dE/dx calibration using simulated and reconstructed muon tracks. A calibration constant Ccal = (5.469 ± 0.003) × 10−3 ADC × tick/e is obtained through a model-dependent calibration process, where 1 tick corresponds to 500 ns of sampling time of an ADC. Furthermore, a calibration technique is presented, demonstrating precise translation from dQ/dx to dE/dx. This calibration method is applied to stopping muons, charged pions, and protons in the DUNE FD, addressing the measurement of energy loss in the detector volume. These are important calibrations of the DUNE FD and will contribute to achieving the exciting physics goals of the experiment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Self-consistent analysis for the η c → γ γ process

The next-to-next-to-leading-order (NNLO) perturbative QCD (pQCD) predictions for both the decay width and the transition form factor in the η c → γ γ process, based on nonrelativistic QCD (NRQCD), deviate from precise experimental measurements. These significant discrepancies have cast doubt on the applicability of NRQCD to charmonium processes. In this paper, we analyze the η c → γ γ process by applying the principle of maximum conformality (PMC), a systematic method for eliminating renormalization scheme-and-scale ambiguities. The PMC renormalization scales are determined by absorbing the nonconformal β -terms that govern the behavior of the QCD running coupling via the renormalization group equation. We obtain the PMC scale Q ⋆ = 4.49 m c for the η c → γ γ decay width. Even after using the PMC method, the convergence of the pQCD series is still poor, which indicates the importance of uncalculated next-to-next-to-next-to-leading-order and higher-order terms. The resulting value for Γ η c → γ γ is in agreement with the Particle Data Group’s reported value of Γ η c → γ γ = 5.1 ± 0.4 keV within the bounds of uncertainties. Moreover, the transition form factor obtained using the PMC is also in good agreement with precise experimental measurements. The application of the PMC suggests a potential resolution to η c → γ γ puzzle and supports the applicability of NRQCD to charmonium processes. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Review of top quark mass measurements in CMS

The top quark mass is one of the most intriguing parameters of the standard model (SM). Its value indicates a Yukawa coupling close to unity, and the resulting strong ties to Higgs physics make the top quark mass a crucial ingredient for understanding essential aspects of the electroweak sector of the SM. This review offers the first comprehensive overview of the top quark mass measurements performed by the CMS Collaboration using the data collected at centre-of-mass energies of 7, 8, and 13 TeV. Moreover, a detailed description of the top quark event reconstruction is provided and dedicated studies of the dominant uncertainties in the modelling of the signal processes are discussed. The interpretation of the experimental results on the top quark mass in terms of the SM Lagrangian parameter is challenging and is a focus of an ongoing discussion in the theory community. The CMS Collaboration has performed two main types of top quark mass measurements, addressing this challenge from different perspectives: highly precise ‘direct’ measurements, based on reconstructed top quark decay products and relying exclusively on Monte-Carlo simulations, as well as ‘indirect’ measurements, where the simulations are employed to determine parton-level cross sections that are compared to fixed-order perturbative calculations. Recent mass extractions using Lorentz-boosted top quarks open a new avenue of measurements based on top quark decay products contained in a single particle jet, with promising prospects for accurate theoretical interpretations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Application and performance of the novel Elcomat 5000 autocollimator in slope-measuring profilometry of beamline optics

Autocollimators are used in profilometers for the precise form measurement of beam-shaping optics for synchrotron light sources and x-ray free-electron lasers. This application requires using an aperture stop, typically 2.5 mm in diameter, which limits the footprint of the autocollimator’s measuring beam on the optics to achieve a sufficiently high lateral resolution. Central to the development of profilometry has been the availability of commercial autocollimators, such as the Elcomat 3000 from Möller–Wedel Optical. Although autocollimators are generally not designed for use with small apertures, this device has proven capable and has become the de facto standard. Now that it has been replaced by the Elcomat 5000, we evaluate the performance of several autocollimators of this type at small apertures, including the characterization of instrument transfer functions with a chirped height profile. We demonstrate that the Elcomat 5000 is capable of repeatable angle measurements with a standard deviation of 0.014 arcsec at an aperture diameter of 1.6 mm, whereas the Elcomat 3000 achieves 0.03 arcsec at 2.5 mm, comparing models with modified reticle designs. Here, we also investigate the influence of optical aberrations of the autocollimator’s objective and their changes with the path length to the surface under test. We characterize the sensitivity of the angle measurement to changes in environmental parameters, in particular, barometric pressure. These efforts are aimed at approaching fundamental limits in the characterization of the shape of optical surfaces with autocollimator-based profilometers so that these are ready for characterizing the next generation of synchrotron and XFEL beamline optics.

angle metrology↗

On Final Results From the Muon $g\mathrm{-}2$ Experiment at Fermilab

The Muon g-2 Experiment at Fermilab has measured the muon anomalous magnetic moment, a_mu, with unprecedented precision, leveraging a dataset from Runs 1 6 that is 21 times larger than its Brookhaven predecessor. This talk will present the experiment s final result, which serves as a benchmark for testing the Standard Model with high precision. The measurement was performed in a storage ring with a highly uniform magnetic field, where precise beam dynamics understanding is vital to determine the muon anomalous precession frequency. Key to this effort were advanced simulation tools including COSY INFINITY, precise fringe field modeling, and calculations of beam dynamics characteristics like tunes and chromaticity. We will conclude by exploring how the experiment's findings reshape our understanding of particle physics.

Valetov, Eremey [Michigan State U.]↗

Toward $\nu_{\mu}$CC $\eta$ Meson Cross Sections on Argon in SBND

The modeling of resonant neutrino interactions on argon is critical for achieving precision neutrino oscillation measurements and searching for physics beyond the Standard Model with both DUNE and the Short-Baseline Neutrino Program. Higher mass resonances beyond the $\Delta$(1232) baryon are particularly poorly constrained experimentally, and yet contribute a significant rate in multi-GeV interactions. The measurement of $\eta$(548) meson production from the decay of these resonances provides a unique probe, as well as the opportunity to measure observables sensitive to final state interactions with the nucleus. This poster will present progress towards the measurement of meson production with the Short-Baseline Near Detector (SBND) at Fermilab, leveraging the clean $\eta \rightarrow \gamma \gamma$ decay channel. The large statistics of the SBND dataset will provide high-precision measurements of this channel capable of constraining uncertainties in the modeling of higher order resonant interactions. This analysis further provides important handles on electromagnetic shower reconstruction performance through evaluation of the 548 MeV $\eta$ invariant mass peak.

Antonakis, Alexander [UC, Santa Barbara]↗