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At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Uplift and Seismicity Driven by Magmatic Inflation at Sierra Negra Volcano, Galápagos Islands

Abstract Although episodes of surface uplift and elevated seismicity precede many volcanic eruptions, their temporal evolution is often complex, and apparently in contradiction to simple trends predicted by mechanical deformation models. Here, we use continuous global positioning system and seismic data recorded at Sierra Negra volcano, Galápagos Islands, to show how the edifice responded to stress changes driven by magma accumulation in a shallow sill. The rate of uplift varied during the 13 years and 6.5 m of inflation before the 2018 eruption. The number of earthquakes per unit of uplift increased exponentially with total uplift as the differential stress increased. Accordingly, the temporal seismicity rate varied in time as a function of both the total uplift and the uplift rate. The Gutenberg‐Richter b ‐value decreased as a function of total uplift. In the final six months before the eruption, a sequence of large ( M > 4) earthquakes regulated the state of stress on the fault, each being followed by 2–3 days of postseismic quiescence, and retarding the increase in seismicity rate. These earthquakes did not affect the overall uplift rate. Subsidence of 8.5 m accompanied the 2‐month eruption. On resumption of uplift, the number of earthquakes per unit of uplift was very low, and the b ‐value high, reflecting the relaxed stress state of the fault system. These observations show that crustal deformation becomes increasingly brittle at higher stress states, and supports theoretical models based on elastic‐brittle mechanics. They suggest that joint interpretation of deformation and seismicity is key for forecasting future eruptions in similar volcanic settings.

Bell, Andrew Forbes↗
DOE OSTI2023

An updated nuclear-physics and multi-messenger astrophysics framework for binary neutron star mergers

The multi-messenger detection of the gravitational-wave signal GW170817, the corresponding kilonova AT2017gfo and the short gamma-ray burst GRB170817A, as well as the observed afterglow has delivered a scientific breakthrough. For an accurate interpretation of all these different messengers, one requires robust theoretical models that describe the emitted gravitational-wave, the electromagnetic emission, and dense matter reliably. In addition, one needs efficient and accurate computational tools to ensure a correct cross-correlation between the models and the observational data. For this purpose, we have developed the Nuclear-physics and Multi-Messenger Astrophysics framework NMMA. The code allows incorporation of nuclear-physics constraints at low densities as well as X-ray and radio observations of isolated neutron stars. In previous works, the NMMA code has allowed us to constrain the equation of state of supranuclear dense matter, to measure the Hubble constant, and to compare dense-matter physics probed in neutron-star mergers and in heavy-ion collisions, and to classify electromagnetic observations and perform model selection. Here, we show an extension of the NMMA code as a first attempt of analyzing the gravitational-wave signal, the kilonova, and the gamma-ray burst afterglow simultaneously. Incorporating all available information, we estimate the radius of a 1.4M ⊙ neutron star to be $R$ $=$ $11.98^{+0.35}_{-0.04}$ km.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

SA-GAT-SR: self-adaptable graph attention networks with symbolic regression for high-fidelity material property prediction

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 × acceleration compared to conventional SR implementations that heavily rely on first-principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Modification of terahertz emission spectrum using microfabricated spintronic emitters

Terahertz (THz) radiation with sub-millimeter wavelength falls in the gap between optical and radio frequencies. Conventional THz emitters do not intertwine with spin degrees of freedom. However, it was recently shown that broadband THz radiation can be efficiently created also by exploiting spin-based effects on ultrafast time scales. Here, we demonstrate the generation and control of THz radiation from microstructured spintronic THz emitters based on the inverse spin-Hall effect. Using time-domain THz spectroscopy, we compare the THz spectra of different stripe patterns made of Fe/Pt bilayers with a spectrum obtained from an extended Fe/Pt bilayer film. It is found that the THz spectrum can be altered by a proper choice of the microstructure dimensions. The experimentally observed spectra are interpreted in terms of a simplified multi-slit interference model, which captures the main experimental features. Our results pave the way for an efficient control of THz light emitted from magnetic heterostructures. This is a crucial step forward for the design and realization of directional THz sources.

Wu, Weipeng↗
DOE OSTI2023

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the “feature importance” approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.

Chemistry↗
DOE OSTI2023

Inference of strength and phase transition kinetics in dynamically-compressed tin

Dynamic compression experiments in condensed matter are of interest in part because they provide opportunities to examine material response under extreme conditions; however, the inference of material behavior from dynamic experiments is challenging in the presence of phase transitions exhibiting kinetic processes. Demonstrating an approach to quantitative interpretation of such dynamic experiments, here we present a Bayesian model calibration of strength and phase transformation parameters to data drawn from pulsed power and gas gun shot experiments. The posterior predictions of the Bayesian model capture the experimental measurements and account for the various uncertainties in the experimental configurations. This holistic approach to model calibration utilizing multiple types of experimental data identifies important cross correlations among kinetics, strength, and the phase boundary. Improved insight into potential sources of current model form error is provided by comparing the differences between calibrations against different subsets of the experimental data.

42 ENGINEERING↗
DOE OSTI2025

Enhancing the accuracy of XPS calculations: Exploring hybrid basis set schemes for CVS-EOMIP-CCSD calculations

Reliable computational methodologies and basis sets for modeling x-ray spectra are essential for extracting and interpreting electronic and structural information from experimental x-ray spectra. In particular, the trade-off between numerical accuracy and computational cost due to the size of the basis set is a major challenge, since molecular orbitals undergo extreme relaxation in the core-hole state. To gain clarity on the changes in electronic structure induced by the formation of a core-hole, the use of sufficiently flexible basis for expanding the orbitals, particularly for the core region, has been shown to be essential. This work focuses on the refinement of core-hole ionized state calculations using the equation-of-motion coupled cluster family of methods through an extensive analysis on the effectiveness of “hybrid” and mixed basis sets. In this investigation, we utilize the CVS-EOMIP-CCSD method in combination and construct hybrid basis sets piecewise from readily available Dunning’s correlation consistent basis sets in order to calculate x-ray ionization energies (IEs) for a set of small gas phase molecules. Our results provide insights into the impact of basis sets on the CVS-EOMIP-CCSD calculations of K-edge IEs of first-row p-block elements. Furthermore, these insights enable us to understand more about the basis set dependence of the core IEs computed and allow us to establish a protocol for deriving reliable and cost-effective theoretical estimates for computing IEs of small molecules containing such elements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Temporal covariation of island arc Sr isotopes and seawater chemistry over the past 2 billion years

The chemical compositions of island arc basalts (IAB) reflect contributions from the mantle as well as fluids and melts from the subducting slab. Addition of radiogenic seawater Sr to oceanic crust through hydrothermal alteration and subsequent subduction is often invoked to explain elevated 87 Sr/ 86 Sr signatures in modern IAB. However, changes in the 87 Sr/ 86 Sr of island arc magmatic rocks through time has not been investigated, limiting our understanding of the factors influencing the Sr budgets of arcs throughout Earth’s history. To address this, we compiled 87 Sr/ 86 Sr values from island arc magmatic rocks ranging in age from modern to Paleoproterozoic, only including data from island arc localities that best preserve initial magmatic 87 Sr/ 86 Sr. Median initial 87 Sr/ 86 Sr values are consistently elevated compared to depleted mantle 87 Sr/ 86 Sr over this period, indicating persistent enrichment in radiogenic Sr in island arcs. Moreover, the elevation in island arc 87 Sr/ 86 Sr relative to the depleted mantle is variable. A notable rise in island arc 87 Sr/ 86 Sr during the late Neoproterozoic coincides with a steep increase in seawater 87 Sr/ 86 Sr and Sr concentration. To investigate this potential connectivity, we modeled the 87 Sr/ 86 Sr of island arc magmas between 0 and 830 Ma with inputs of depleted mantle 87 Sr/ 86 Sr, seawater 87 Sr/ 86 Sr, and seawater Sr concentration. The model reproduces the overall trajectory of the compiled data. We interpret the observed temporal variation in island arc 87 Sr/ 86 Sr values and its close association with fluctuations in seawater chemistry as evidence that changes in marine geochemistry have strongly influenced the Sr isotopic record of island arc magmas over time.

Science & Technology - Other Topics↗
DOE OSTI2026

Deployment of Traditional and Hybrid Machine Learning for Critical Heat Flux Prediction in the CTF Thermal-Hydraulics Code

Critical heat flux (CHF) marks the transition from nucleate to film boiling, where heat transfer to the working fluid can rapidly deteriorate. Accurate CHF prediction is essential for efficiency, safety, and preventing equipment damage, particularly in nuclear reactors. Although widely used, empirical correlations frequently exhibit discrepancies when compared to experimental data, limiting their reliability in diverse operational conditions. Traditional machine learning (ML) approaches have demonstrated potential for CHF prediction but often suffer from limited interpretability, data scarcity, and insufficient knowledge of physical principles. Hybrid model approaches, which combine data-driven ML with base models, mitigate these concerns by incorporating prior knowledge of the domain. This study integrates an externally trained purely data-driven ML model and two hybrid models (using the Biasi and Bowring CHF correlations) within the CTF subchannel code via a custom Fortran framework. Performance was evaluated using two validation cases: a subset of the Nuclear Regulatory Commission (NRC) CHF database and the Bennett dryout experiments. In both cases, the hybrid models demonstrated significantly lower error metrics compared to conventional empirical correlations, with the best models often reducing relative error by about 5 percentage points. The pure ML model achieved comparable accuracy, outperforming the hybrid Biasi model in the NRC test case (3.3% versus 5.5% relative error) but exhibiting slightly higher error against the hybrid Bowring model in the Bennett test case (7.7% versus 6.1%). Trend analysis of error parity indicated that ML-based models reduced the tendency for CHF overprediction, improving overall accuracy. These results demonstrate that ML-based CHF models can be effectively integrated into subchannel codes and could potentially increase performance compared to conventional methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Inferring Neutron Star Merger Ejecta Morphology with Kilonovae

In this study we incorporate a new grid of kilonova simulations produced by the Monte Carlo radiative transfer code SuperNu in an inference pipeline for astrophysical transients and evaluate their performance. These simulations contain four different two-component ejecta morphology classes. We analyze follow-up observational strategies by Vera Rubin Observatory in optical and James Webb Space Telescope (JWST) in mid-infrared (MIR). Our analysis suggests that, within these strategies, it is possible to discriminate between the four different morphologies only when late-time JWST observations in MIR are available. We conclude that follow-ups by the new Vera Rubin Observatory alone are not sufficient to determine ejecta morphology. Additionally, we make comparisons between surrogate models based on radiative transfer simulation grids by SuperNu and POSSIS, by analyzing the historic kilonova AT2017gfo that accompanied the gravitational wave event GW170817. We show that both SuperNu and POSSIS models provide similar fits to photometric observations but their qualitative interpretations differ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Impact of Blast Overpressure on the Pharmacokinetics of Various Antibiotics in Sprague Dawley Rats

ABSTRACT Introduction Combat injuries are complex and multimodal. Most injuries to the extremities occur because of explosive devices such as improvised explosive devices. Blast exposure dramatically increases the risk of infection in combat wounds, and there is limited available information on the best antibiotic treatments for these injuries. We previously demonstrated that mice exposed to blast displayed a delayed clearance of cefazolin from the plasma and liver; further semi-mechanistic modeling determined that cefazolin concentrations in the skin of these mice were reduced. Our objective was to investigate the effects of blast on the pharmacokinetics of antibiotics of different types used for the treatment of combat wounds in the rat model. Materials and Methods Male Sprague Dawley rats were exposed to blast overpressure followed by injection of a bolus of animal equivalent doses of an antibiotic (cefazolin, cefepime, ertapenem, or clindamycin) into the tail vein at 1-hour post-blast exposure. Blood was collected at predetermined time points via repeated sampling from the tail vein. Animals were also euthanized at predetermined time points, at which time liver, kidney, skin, and blood via cardiac puncture were collected. Antibiotic concentrations were determined by ultra-performance liquid chromatography–tandem mass spectrometry. Results Blast-exposed rats exhibited a similar rate of clearance compared to non-blasted rats in the blood, liver, kidney, and skin, which is inconsistent with the data regarding cefazolin in blast-exposed mice. Conclusions Our results in rats do not recapitulate our previous observation of delayed cefazolin clearance in mice following the blast overpressure exposure. Although using rats permitted us to collect multiple blood samples from the same animals, rats may not be a suitable model for measuring the pharmacokinetics of antibiotics following blast. The interpretation of the results may be challenging because of variation in data among rat subjects in the same sample groups.

General & Internal Medicine↗
DOE OSTI2020

Concordance cosmology?

ABSTRACT We propose a new intuitive metric for evaluating the tension between two experiments, and apply it to several data sets. While our metric is non-optimal, if evidence of tension is detected, this evidence is robust and easy to interpret. Assuming a flat Lambda cold dark matter (ΛCDM) cosmological model, we find that there is a modest 2.2σ tension between the Dark Energy Survey (DES) Year 1 results and the Planck measurements of the cosmic microwave background. This tension is driven by the difference between the amount of structure observed in the late-time Universe and that predicted from fitting the Planck data, and appears to be unrelated to the tension between Planck and local estimates of the Hubble rate. In particular, combining DES, baryon acoustic oscillations, big bang nucleosynthesis, and supernovae measurements recover a Hubble constant and sound horizon consistent with Planck, and in tension with local distance–ladder measurements. If the tension between these various data sets persists, it is likely that reconciling all current data will require breaking the flat ΛCDM model in at least two different ways: one involving new physics in the early Universe, and one involving new late-time Universe physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Real-space inversion and super-resolution of ultrafast scattering

Ultrafast scattering using x-rays or electrons is an emerging method to obtain structure dynamics at the atomic lengthscales and timescales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector range and the probe energy. So, as a result, the time-resolved signal interpretation is mostly done in reciprocal space and relies on modeling and simulations of specific structures and processes. Here, we introduce a model-free approach to directly resolve scattering signals in real space, surpassing the diffraction limit, using scattering kernels and signal priors that naturally arise from the measurement constraints. We demonstrate the approach on simulated and experimental data, recover multiple atomic motions at sub-angstrom resolutions, and discuss the recovery accuracy and resolution limits versus signal fidelity. The approach offers a robust path to obtain high-resolution real-space information of atomic-scale structure dynamics using current time-resolved x-ray or electron scattering sources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Polarization-resolved core exciton dynamics in LiF using attosecond transient absorption spectroscopy

The ability to control absorption by modifying the polarization of light presents an exciting opportunity to experimentally determine the orbital alignment of absorption features. Here, attosecond extreme ultraviolet (XUV) transient absorption spectroscopy is used to investigate the polarization dependence of core exciton dynamics in LiF thin films at the Li + K edge. XUV pulses excite electrons from the Li 1s core level into the conduction band, allowing for the formation of a p-orbital-like core exciton, aligned along the XUV light polarization axis. A sub-5 fs near-infrared (NIR) probe pulse then arrives at variable time delays, perturbing the XUV-excited states and allowing the coherence decay of the core exciton to be mapped. The coherence lifetimes are found to be ≈ 2.4 ± 0.4 fs, which is attributed to a phonon-mediated dephasing mechanism as in previous core exciton studies. The differential absorption features are also shown to be sensitive to the relative polarization of the XUV and NIR fields. The parallel NIR probe induces couplings between the initial XUV-excited p-like bright exciton and s-like dark excitons. When crossed pump and probe polarizations are used, the coupling between the bright and dark states is no longer dipole-allowed, and the transient absorption signal associated with the coupling is suppressed by approximately 90%. This interpretation is supported by simulations of a few-level model system, as well as analysis of the calculated band structure. Here, the results indicate that laser polarization can serve as a powerful experimental tool for exploring the orbital alignment of core excitonic states in solid-state materials.

Attosecond laser spectroscopy↗
DOE OSTI2020

Shape evolution of neutron-rich 106,108,110 Mo isotopes in the triaxial degree of freedom

Background: Neutron-rich nuclei with mass number between 100 and 110 attract much attention, since several kinds of shapes, such as spherical, prolate, oblate, and triaxial shapes, are predicted. In particular, for neutron-rich Mo isotopes, different models predict different magnitudes and rigidity of triaxial deformation. Previous interpretations of experimental results based solely on low-lying $2^+_2$ states are insufficient to distinguish between the rigid triaxial shape, $\gamma$ vibration, or $\gamma$-soft rotor. Purpose: The shape evolution of 106 Mo, 108 Mo, and 110 Mo is investigated through their $2^+_1$-state lifetimes, decay-branching ratios of the $2^+_2$ state, and energies of the low-lying collective excited states with $K^π = 0^+, 2^+$, and $4^+$. Method: $\beta$-delayed $\gamma$-ray spectroscopy was employed for neutron-rich Nb and Zr isotopes produced at the RIKEN RI Beam Factory to populate excited states in 106 Mo, 108 Mo, and 110 Mo. The EUroball-RIKEN Cluster Array was used for high-resolution $\gamma$-ray detection and lifetimes of the $2^+_1$ states were determined using the UK fast-timing array of LaBr 3 (Ce) detectors. Results: New $\gamma$-ray transitions and levels are reported, including newly assigned $0^+_2$ states in 108,110 Mo. Quadrupole deformations were obtained for 106,108,110 Mo from their $2^+_1$ energies and lifetimes. The $\beta$-delayed neutron-emission probabilities of 108 Nb and 110 Nb were determined by examining the $\gamma$ rays of their respective daughter decays. Conclusions: In this work, the even-odd energy staggering in the $2^+_2$ band was compared with typical patterns of the $\gamma$-vibrational band, rigid triaxial rotor, and $\gamma$-soft rotor. The very small even-odd staggering of 106 Mo, 108 Mo, and 110 Mo favors a $\gamma$-vibrational band assignment. The kinematic moment of inertia for the $2^+_2$ band showed a trend similar to the ground-state band, which is as expected for the $\gamma$-vibrational band. Beyond-mean-field calculations employing the constrained Hartree-Fock-Bogoliubov and local quasiparticle-random-phase approximation method using the SLy5 + T interaction reproduced the ground and $2^+_2$ bands in 106 Mo and 108 Mo. The collective wave functions are consistent with the interpretation of the $2^+_2$ band as the $\gamma$-vibrational band of the prolate shape. However, the staggering pattern observed in 110 Mo differs from the one suggested in the calculations which predict a $\gamma$-soft rotor. There was no experimental indication of the oblate shape or the $\gamma$-soft rotor predicted in these Mo isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Octupole correlations near Te 110

The lifetime of the 2 + and 9 – , 11 – , 13 – , 15 – states in the neutron-deficient 110 Te was measured for the first time using the recoil distance Doppler shift technique. The reported value of the reduced transition probability B(E2; $0$$^{+}_{g.s}$ → 2 + ) = 4.3(8) × 10 3 e 2 fm 4 supports the systematic for even-mass Te isotopes and was interpreted in the framework of the large-scale shell model and cranked shell model calculations. The measured reduced transition probabilities in the negative-parity yrast band revealed the upward trend towards the high spins. Furthermore, the enhanced collectivity is discussed in terms of the tilted axis cranking approach and the symmetry configuration mixing method with the Gogny D1S interaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Search for electroweak production of charginos and sleptons decaying into final states with two leptons and missing transverse momentum in $$\sqrt{s}=13$$s=13 $$\text {TeV}$$TeV pp collisions using the ATLAS detector

© 2020, CERN for the benefit of the ATLAS collaboration. A search for the electroweak production of charginos and sleptons decaying into final states with two electrons or muons is presented. The analysis is based on 139 fb- 1 of proton–proton collisions recorded by the ATLAS detector at the Large Hadron Collider at s=13 TeV. Three R-parity-conserving scenarios where the lightest neutralino is the lightest supersymmetric particle are considered: the production of chargino pairs with decays via either W bosons or sleptons, and the direct production of slepton pairs. The analysis is optimised for the first of these scenarios, but the results are also interpreted in the others. No significant deviations from the Standard Model expectations are observed and limits at 95% confidence level are set on the masses of relevant supersymmetric particles in each of the scenarios. For a massless lightest neutralino, masses up to 420 Ge are excluded for the production of the lightest-chargino pairs assuming W-boson-mediated decays and up to 1 TeV for slepton-mediated decays, whereas for slepton-pair production masses up to 700 Ge are excluded assuming three generations of mass-degenerate sleptons.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Search for R-parity-violating supersymmetry in a final state containing leptons and many jets with the ATLAS experiment using $\sqrt{s}=13\hbox{TeV}$ proton–proton collision data

A search for R-parity-violating supersymmetry in final states characterized by high jet multiplicity, at least one isolated light lepton and either zero or at least three b-tagged jets is presented. The search uses 139fb –1 of $\sqrt{s}=13\hbox{TeV}$ proton–proton collision data collected by the ATLAS experiment during Run 2 of the Large Hadron Collider. The results are interpreted in the context of R-parity-violating supersymmetry models that feature gluino production, top-squark production, or electroweakino production. The dominant sources of background are estimated using a data-driven model, based on observables at medium jet multiplicity, to predict the b-tagged jet multiplicity distribution at the higher jet multiplicities used in the search. Machine-learning techniques are used to reach sensitivity to electroweakino production, extending the data-driven background estimation to the shape of the machine-learning discriminant. No significant excess over the Standard Model expectation is observed and exclusion limits at the 95% confidence level are extracted, reaching as high as 2.4 TeV in gluino mass, 1.35 TeV in top-squark mass, and 320 (365) GeV in higgsino (wino) mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗