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At least 1,315 records · Page 73

Interactive computer graphic surface modeling of three-dimensional solid domains for boundary element analysis

The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.

Perucchio, R.↗

Analysis of gas storage and transport in Eagle Ford shale using pressure pulse decay measurements with He, Kr and CO 2

Detailed characterization of gas transport and storage in low-permeability and organic-rich shales is associated with an array of challenges due to the complex morphology of the pore space, representing a broad range of pore sizes, combined with the heterogeneous fabric of the shale matrix. These factors, and their interplay during gas transport and sorption, complicate a) the analysis of shale samples at the laboratory scale (~ up to a ft. In length), and b) the prediction of natural gas production and carbon sequestration potential at larger scales. Here, in this work, tandem experiments with inert (helium – He) and adsorbing (krypton - Kr and carbon dioxide - CO 2 ) gases were performed and analyzed to develop an efficient workflow for characterizing and modeling transport and sorption at the laboratory scale. In particular, pressure pulse-decay (PPD) measurements were conducted on an Eagle Ford shale core sample at room temperature using He, Kr, and CO 2 . PPD measurements with He (a non-sorbing gas) were employed to probe the overall porosity, including natural fractures, microcracks, mesopores, and micropores. A triple-porosity model (TPM) was adopted to interpret the gas transport in the shale sample: The pore space is represented by three interacting continua, including macropores (larger fractures), mesopores (including microcracks), and micropores. To facilitate the application of the TPM, a modified analytical approach is introduced to extract effective transport parameters (in terms of the characteristic time for transport at relevant porosity levels) directly from the PPD measurements with He. To validate the modeling approach, model parameters extracted from two He PPD measurements are demonstrated to provide excellent agreement with a 3rd He PPD measurement performed at a higher pressure. The effective transport parameters, extracted from the He experiments, were subsequently converted for application to the Kr and CO 2 PPD experiments, by accounting for relevant transport modes and differences in fluid properties. Excess adsorption isotherms were extracted from the equilibrium pressures of the Kr and CO 2 PPD experiments using the He pore volume as a baseline. These adsorption isotherms were then integrated into the TPM to predict combined gas transport and sorption for Kr and CO 2 , with transport coefficients translated from the He measurements. The predictions for Kr and CO 2 are demonstrated to be in excellent agreement with the experimental observations. This, in turn, demonstrates that the proposed analytical approach provides for an effective characterization of mass transfer rates in shales, that can be applied directly in a TPM representation of mass transfer and sorption.

58 GEOSCIENCES↗

AMMPER: a user-friendly agent-based model that recapitulates simple metabolic responses of yeast to deep-space radiation

For humans venturing to deep space, radiation exposure poses a major health risk. Fundamental research into the biological effects of space radiation are essential for enabling exploration, and the first experimental organisms we send to deep space will be microbial. Yet there are many ways in which microorganisms are likely to experience the effects of high-energy particle radiation (such as Galactic Cosmic Rays) differently from multicellular animals, partly due to the simple fact that microbes are small and unicellular-- less likely to get hit in the first place, and less likely to communicate damage between cells. Computational modeling can aid in designing experiments and predicting the biological effects of radiation, but thus far particle radiation models have not focused on microbes. Here we present the latest developments in AMMPER, the Agent-based Model for Microbial Populations Exposed to Radiation. Originally written in 2021, AMMPER is a Python-based model that incorporates radiation track data from NASA's RITRACKS software and simulates the growth, damage, and death of yeast cells in 3D. It is now freely available as an open-source package on NASA's GitHub repository. Recent improvements include the ability to simulate the dynamics of alamarBlue, a color-changing redox dye commonly used to track metabolic activity in microbial spaceflight experiments. We demonstrate that a simple blue-pink-clear transition model is able to recapitulate key features observed in empirical data from ground studies. AMMPER also includes a new graphical user interface and introductory tutorial to facilitate ease of use by a wider audience. AMMPER can help us to understand how spatially heterogeneous particle radiation damage at the single-cell level can translate to growth differences at the population level, ultimately allowing us to better interpret experiments using microbes as model organisms and how well their results apply to humans.

yeast↗

Properties of nearby interstellar hydrogen deduced from Lyman-alpha sky background measurements

For a sufficiently rapid relative motion of the solar system and the nearby interstellar gas, neutral atoms may be expected to penetrate the heliosphere before becoming ionized. Recent satellite measurements of the Lyman alpha emission above the geocorona indicate such an interstellar wind of neutral hydrogen emerging from the direction of Sagittarius and reaching to within a few astronomical units of the sun. A detailed model of the scattering of solar Lyman alpha from the spatial distribution of neutral hydrogen in interplanetary space is presented. This asymmetric distribution is established by solar wind and solar ultraviolet ionization processes along the trajectories of the incoming hydrogen atoms. The values of the interstellar density, the relative velocity, and the gas temperature are adjusted to agree with the Lyman alpha measurements. The results may be interpreted in terms of two models, the cold model and the hot model of the interstellar gas, depending on whether galactic Lyman alpha emission is present at its maximum allowable value or negligibly small.

Thomas, G. E.↗

Relativistic particle acceleration in plerions

We discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized -- the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put approximately 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) varies as E(exp -2), where N(E)dE is the number of particles with energy between E and E+dE. The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be gamma(sub +/-)m(sub +/-)c squared = m(sub i)c squared gamma(sub 1)/Z(sub i), where gamma(sub 1) is the Lorentz factor of the upstream flow and Z(sub i) is the atomic number of the ions. The shock's spatial structure is shown to contain a series of 'overshoots' in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the 'wisps,' surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure gamma(sub 1) and a number of other properties of the pulsar's wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.

Arons, Jonathan↗

Photoionization models for the winds from cataclysmic variables

Photoionization models are presented for the relative abundances of Si IV, C IV, and N V as a function of the ionization parameter and shape of the ionizing continuum spectrum in the EUV and X-ray energy range. These models are applied to the interpretation of the UV resonance lines observed from the cataclysmic variable TW Virginis by Cordova and Mason. The observed lines are assumed to be formed in gas flowing supersonically out from the continuum source in the form of a stellar wind. It is shown that the shape of the ionizing spectrum can be determined without assuming that the outflow is spherical by fitting to ratios of the line strengths. Models which fit the observed ratios include an X-ray continuum with a low-energy cutoff and may also include a lower luminosity component in the EUV spectral region. Under the added assumption of spherical outflow the derived ionization parameter for the X-ray component can be used to constrain the total mass flux in the wind.

Kallman, T. R.↗

Exploring the Relative Importance of the MJO and ENSO to North Pacific Subseasonal Predictability

Abstract Here we explore the relative contribution of the Madden‐Julian Oscillation (MJO) and El Niño Southern Oscillation (ENSO) to midlatitude subseasonal predictive skill of upper atmospheric circulation over the North Pacific, using an inherently interpretable neural network applied to pre‐industrial control runs of the Community Earth System Model version 2. We find that this interpretable network generally favors the state of ENSO, rather than the MJO, to make correct predictions on a range of subseasonal lead times and predictand averaging windows. Moreover, the predictability of positive circulation anomalies over the North Pacific is comparatively lower than that of their negative counterparts, especially evident when the ENSO state is important. However, when ENSO is in a neutral state, our findings indicate that the MJO provides some predictive information, particularly for positive anomalies. We identify three distinct evolutions of these MJO states, offering fresh insights into opportune forecasting windows for MJO teleconnections.

58 GEOSCIENCES↗

Energy partitioning in the Io plasma torus

The Io plasma torus, which emits substantial amounts of EUV radiation from multiply ionized oxygen and sulfur, represents one of the significant discoveries of the Voyager 1 mission. The present study is concerned with the effects of various physical processes on the density and energy partitioning of the Io plasma torus. For the ions the dominant effects, which have different relative importance in different parameter regimes, are electron impact ionization, charge exchange, electron-ion collisions, and confinement time loss. Attention is given to a physical model, the solution of the quasi-linear equations, the obtained results, and an interpretation of observations in relation to the model results.

Smith, R. A.↗

Supra Arcade Downflows with XRT Informed by Dipolarization Fronts with THEMIS

Magnetic reconnection can rapidly reconfigure the magnetic field of the corona, accelerating plasma through the site of reconnection. Ambiguities due to the nature of remote sensing have complicated the interpretation of observations of the inflowing and outflowing plasma in reconnecting regions. In particular, the interpretation of sunward moving density depletions above flare arcades (known as Supra Arcade Downflows - SADs) is still debated. Hinode/XRT has provided a wealth of observations for SADs and helped inform our current understanding of these structures. SADs have been interpreted as wakes behind newly reconnected and outflowing loops (Supra Arcade Downflowing Loops - SADLs). Models have shown the plausibility of this interpretation, though this interpretation has not yet been fully accepted. We present here observations of newly reconnected outflowing loops observed via in situ instruments in the magnetosphere. These observations, provided by five THEMIS spacecraft, show that around retracting loops (dipolarization fronts in this context) similar dynamic temperature and density structures are found as seen in SADs. We compare data from multiple SADs and dipolarization fronts to show that the observational signatures implied in the corona can be directly observed in similar plasma regimes in the magnetosphere, strongly favoring the interpretation of SADs as wakes behind retracting loops.

magnetism↗

Supra Arcade Downflows with XRT Informed by Dipolarization Fronts with THEMIS

Magnetic reconnection can rapidly reconfigure the magnetic field of the corona, accelerating plasma through the site of reconnection. Ambiguities due to the nature of remote sensing have complicated the interpretation of observations of the inflowing and outflowing plasma in reconnecting regions. In particular, the interpretation of sunward moving density depletions above flare arcades (known as Supra Arcade Downflows - SADs) is still debated. Hinode/XRT has provided a wealth of observations for SADs and helped inform our current understanding of these structures. SADs have been interpreted as wakes behind newly reconnected and outflowing loops (Supra Arcade Downflowing Loops - SADLs). Models have shown the plausibility of this interpretation, though this interpretation has not yet been fully accepted. We present here observations of newly reconnected outflowing loops observed via in situ instruments in the magnetosphere. These observations, provided by five THEMIS spacecraft, show that around retracting loops (dipolarization fronts in this context) similar dynamic temperature and density structures are found as seen in SADs. We compare data from multiple SADs and dipolarization fronts to show that the observational signatures implied in the corona can be directly observed in similar plasma regimes in the magnetosphere, strongly favoring the interpretation of SADs as wakes behind retracting loops.

corona↗

Combination of searches for invisible decays of the Higgs boson using 139 fb –1 of proton-proton collision data at $\sqrt{s}$ TeV collected with the ATLAS experiment

Many extensions of the Standard Model predict the production of dark matter particles at the LHC. Sufficiently light dark matter particles may be produced in decays of the Higgs boson that would appear invisible to the detector. This Letter presents a statistical combination of searches for $H$ → invisible decays where multiple production modes of the Standard Model Higgs boson are considered. These searches are performed with the ATLAS detector using 139 fb –1 of proton–proton collisions at a centre–of–mass energy of $\sqrt{s}$ = 13 TeV at the LHC. In combination with the results at $\sqrt{s}$ = 13 TeV and 8 TeV, an upper limit on the $H$ → invisible branching ratio of 0.107 (0.077) at the 95% confidence level is observed (expected). These results are also interpreted in the context of models where the 125 GeV Higgs boson acts as a portal to dark matter, and limits are set on the scattering cross-section of weakly interacting massive particles and nucleons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Thermodynamic constraints on the textural evolution of eucrite, EET 90020

Basaltic eucrites, which are possibly parts of the Vestan crust, formed as either lava flows or intrusions, and can offer insights into early crust formation. However most eucrites have experienced thermal metamorphism, which exacerbates the challenges of understanding these samples. A variety of petrogenetic models such as, partial melting of a primitive source, fractional crystallization of magmas emplaced in a primitive crust, and/or partial melting of a eucritic source coupled with melt mixing and assimilation have been proposed in order to explain observed petrologic and chemical characteristics of eucrites. EET 90020 is an unbrecciated eucrite that has experienced significant thermal metamorphism, with temperatures of metamorphic equilibration calculated to be ~840-1040°C. Its petrologic history remains contentious, in part due to differences in trace element analyses [10,17, this work], which has led to multiple metamorphic interpretations [8,10-11]. Here, we combined petrologic observations, chemical analyses, and thermodynamic modeling, to interpret micro-domain textures identified in EET 90020 and better constrain its petrologic history. Ultimately, the development of such textures is a direct result of the geologic processes operating on a young Vesta or similar asteroid. Sample description: We identified three textural domains in EET 90020 (Figure 1); (I) A coarse grain domain with granoblastic plagioclase and pyroxene, (II) a medium grain domain with curved grain boundaries between plagioclase and pyroxene, and (III) a fine grain domain dominated by tridymite that fills in interstitial space between spherical plagioclase. Major element chemistry in phases is consistent across domains. Pyroxene have distinctive high Ca lamellae (Wo40.92En28.1Fs31.0) forming from the low-Ca pigeonite host (Wo3.5En33.7Fs62.8). There are small amounts of fayalitic olivine along pyroxene/oxide grain boundaries, where pyroxenes have reacted with ilmenite/chromite clasts. Plagioclase is anorthitic (Avg ~An88), with little variation (An86-92.5). Trace element bulk rock analyses were collected via ICP-MS and individual mineral analyses with LA-ICP-MS (Figure 2). The bulk sample has an observable enrichment in light rare earth elements, with a notable depletion in Eu. Plagioclase is enriched in LREEs, depleted in HREEs, and has a positive Eu anomaly while pyroxene is enriched in HREEs with a negative Eu anomaly. Variations in trace element analyses is likely influenced by the presence of phosphates because are highly enriched in REEs and have a dramatic effect on the bulk domain compositions. Thermodynamic modeling: The software package, Perple_X, was used to calculate mineral phase equilibria over a range of conditions using a Gibbs free energy minimization approach [12]. Models used all major/minor elements except P2O5. Thermodynamic properties from [13] were used to constrain endmember phase stabilities. Activity models were used to describe mixing in phases with solid solution. Isochemical P-T phase diagrams were constructed for the bulk thin section, and the coarse, medium and fine grain domain compositions. Domain compositions were determined using microprobe analyses of phases identified in each domain and observed modal mineral abundancies. Thermodynamically stable pyroxene compositions were extracted from model results and compared to pyroxene compositions collected via EMPA, allowing us to calculate temperatures for metamorphic equilibrium. Results: Results that use the coarse domain composition (Fig. 3a) demonstrate overlap at T ~ 1020°C indicating high T equilibration. There was no overlap for the medium and fine grain domains, or the bulk composition (e.g., Fig. 3b) indicating that these are not equilibrium assemblages. These results were replicated using data from [8,20]. Discussion: The disequilibrium results from the bulk rock, fine grain and medium grain models imply that EET 90020 was modified during and/or after peak metamorphism (open system behavior). However, this is in contrast to the coarse domain where it appears as if equilibrium was maintained. We suggest that this conflict is explained by highly localized equilibrium occurring at millimeter length-scales, which has been observed in terrestrial metamorphism where aqueous fluid infiltrate [14] or melt loss occurs [15]. It is unlikely that aqueous alteration was significant in modifying the bulk composition of EET 90020, because it lacks hydrated minerals. However, the presence of melt is supported by the presence of an abundance of curved grain boundaries and spherical grains in the medium and fine grain domains This contrasts the coarse domain, where grain boundaries are angular. Given the evidence for disequilibrium in the medium and fine grain domains, it would be inappropriate to draw additional conclusions about textural evolution using thermodynamic models of those domains. However, modeling results of the coarse grain domain, where equilibrium was maintained, can provide useful insights into the geologic evolution of EET 90020. We approximate maximum metamorphic temperatures, using the Ca component in pyroxene, at ~1020°C (Fig. 4), which is consistent with previous two-pyroxene thermometry [11]. At this temperature, up to 10 vol % melt can be produced in the coarse grain domain, which is at the boundary of minimum melt needed in order to segregate and form a melt network [16]. Tridymite and plagioclase would be the first minerals to melt out during heating starting ~990°C. This is consistent with the observed melt textures formed by tridymite and plagioclase in the fine grain domain. We suggest that a partial melting model best explains the textural development of EET 90020. Upon heating, melt generated was either trapped, resulting in no net change in the localized rock composition, or migrated, resulting in disequilibrium between pyroxene and the surrounding matrix. A positive Eu anomaly in plagioclase indicates that all of the plagioclase was melted previously. This is consistent with previous studies that have suggested that EET 90020 represents a residual eucrite that experienced partial melting and subsequent melt loss [8]. We speculate that partial melting could have occurred when EET 90020 was heated in the asteroid’s lower crust or adjacent to an intrusion [7]. Future work will study other, texturally heterogeneous samples to see if EET 90020 presents a unique circumstance or whether crustal partial melting was ubiquitous on the eucrite asteroid.

Eucrites↗

Physical interpretation of variations in total solar irradiance

Radiometry from the Solar Maximum Mission and Nimbus 7 satellites has demonstrated that the solar constant varies at a peak-to-peak level of up to 0.2 percent on time scales of weeks. The rotation and evolution of dark spots and bright faculae across the sun's disk accounts for most of that variation. Reasonable explanations have been put forward to explain how the spot-blocked heat flow might be stored, and to explain the source of the intense radiation that gives rise to the increased irradiance produced by the bright magnetic faculae. Time-dependent models of the response of the solar convection zone to small perturbations also indicate that slower variations in total solar irradiance of comparable magnitude are likely. More precise observations of the total solar irradiance and radius over long time scales are required to demonstrate the existence of such climatologically relevant changes, and to test models that would enable the interpretation and prediction of these changes.

Foukal, P.↗

Passive microwave remote sensing of an anisotropic random-medium layer

The principle of reciprocity is invoked to calculate the brightness temperatures for passive microwave remote sensing of a two-layer anisotropic random medium. The bistatic scattering coefficients are first computed with the Born approximation and then integrated over the upper hemisphere to be subtracted from unity, in order to obtain the emissivity for the random-medium layer. The theoretical results are illustrated by plotting the emissivities as functions of viewing angles and polarizations. They are used to interpret remote sgnsing data obtained from vegetation canopy where the anisotropic random-medium model applies. Field measurements with corn stalks arranged in various configurations with preferred azimuthal directions are successfully interpreted with this model.

Lee, J. K.↗

Accurate noncovalent interactions in atomistic systems via quantum Drude oscillators

Accurately modeling polarization and van der Waals (vdW) interactions in atomistic systems typically requires high-level quantum-mechanical methods that are computationally expensive, hence limited in applicability. To address this challenge, efficient yet physically grounded models are needed—ones that not only enable accurate predictions but also provide insight into how noncovalent interactions scale in complex molecular and material systems. This review highlights the quantum Drude oscillator (QDO) model, a physically motivated and computationally efficient framework that captures the essential features of electronic response, including polarization and dispersion forces, across a wide range of chemical and material systems. We discuss how the QDO model quantitatively reproduces the polarization response of many-electron atoms and how key components of noncovalent interactions—exchange-repulsion, polarization, and dispersion—emerge naturally in QDO dimers. Furthermore, the model provides predictive scaling laws that elucidate trends in polarizability and dispersion across the periodic table and in molecular assemblies. By uniting interpretability, accuracy, and efficiency, the QDO model offers a versatile approach for modeling noncovalent interactions in systems ranging from isolated molecules to complex condensed phases and nanostructured materials.

Khabibrakhmanov, Almaz [Univ. of Luxembourg, Luxem↗

Spectral classification of emission-line galaxies

A revised method of classification of narrow line active galaxies and H II region-like galaxies is proposed. It involves the line ratios (O III) lambda 5007/H beta, (N II) lambda 6583/H alpha, (S II) (lambda lambda 6716 = 6731)/H alpha, and (O I) lambda 6300/H alpha. These line ratios take full advantage of the physical distinction between the two types of objects and minimize the effects of reddening correction and errors in the flux calibration. Large sets of internally consistent data are used including new previously unpublished measurements. Prediction of recent photoionization models by power law spectra and by hot stars are compared with the observations. The classification is based on the observational data interpreted on the basis of these models.

Veilleux, Sylvain↗

Spin Change of Asteroid 2012 TC4 Probably by Radiation Torques

Asteroid 2012 TC4 is a small (∼10 m) near-Earth object that was observed during its Earth close approaches in 2012 and 2017. Earlier analyses of light curves revealed its excited rotation state. We collected all available photometric data from the two apparitions to reconstruct its rotation state and convex shape model. We show that light curves from 2012 and 2017 cannot be fitted with a single set of model parameters; the rotation and precession periods are significantly different for these two data sets, and they must have changed between or during the two apparitions. Nevertheless, we could fit all light curves with a dynamically self-consistent model assuming that the spin states of 2012 TC4 in 2012 and 2017 were different. To interpret our results, we developed a numerical model of its spin evolution in which we included two potentially relevant perturbations: (i) gravitational torque due to the Sun and Earth and (ii) radiation torque, known as the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. Despite our model simplicity, we found that the role of gravitational torques is negligible. Instead, we argue that the observed change of its spin state may be plausibly explained as a result of the YORP torque. To strengthen this interpretation, we verify that (i) the internal energy dissipation due to material inelasticity and (ii) an impact with a sufficiently large interplanetary particle are both highly unlikely causes of its observed spin state change. If true, this is the first case where the YORP effect has been detected for a tumbling body.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Search for dark QCD with emerging jets in proton-proton collisions at $ \sqrt{s} $ = 13 TeV

A search for “emerging jets” produced in proton-proton collisions at a center-of-mass energy of 13 TeV is performed using data collected by the CMS experiment corresponding to an integrated luminosity of 138 fb$^{−1}$. This search examines a hypothetical dark quantum chromodynamics (QCD) sector that couples to the standard model (SM) through a scalar mediator. The scalar mediator decays into an SM quark and a dark sector quark. As the dark sector quark showers and hadronizes, it produces long-lived dark mesons that subsequently decay into SM particles, resulting in a jet, known as an emerging jet, with multiple displaced vertices. This search looks for pair production of the scalar mediator at the LHC, which yields events with two SM jets and two emerging jets at leading order. The results are interpreted using two dark sector models with different flavor structures, and exclude mediator masses up to 1950 (1950) GeV for an unflavored (flavor-aligned) dark QCD model. The unflavored results surpass a previous search for emerging jets by setting the most stringent mediator mass exclusion limits to date, while the flavor-aligned results provide the first direct mediator mass exclusion limits to date.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗