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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Adaptive Stiffness Power Take-Off System for a Hydraulic Hose-Pump Point Absorber Wave Energy Converter

Two crucial challenges faced in the design of ocean wave energy converters (WECs) are maintaining high capacity factors and remaining robust in everchanging, harsh ocean environments. This study introduces a novel mechanism for achieving reactive WEC control with a soft hydraulic power take-off, thereby addressing both challenges. The device of interest involves a hydraulic pump, constructed from a fluidic flexible matrix composite (F2MC), which is cyclically stretched by driving waves and pressurizes working fluid through a turbine-generator. This class of fiber-reinforced stretch hoses is established for ocean use as robust moorings and shock absorbers. The dynamic properties of the F2MC pump depend on internal pressure, which can be controlled by a continuously variable transmission between the turbine and generator, allowing the system to be adapted for better performance over a wide range of wave conditions. This work presents a dynamic model for operation and adaptive behavior of this power take-off system, experimentally validates components of the model, and performs dynamic simulations of the system that show increases in power production and capacity factor compared to non-adaptive operation for a variety of driving wave conditions. This work develops the basis for future large-scale experimental testing and controller design of this system.

Wave energy conversion, fluidic flexible matrix co↗
DOE OSTI2022

Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm

The trading of fidelity for scale enables approximate classical simulators such as matrix product states (MPSs) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $\mathcal{χ}$ for MPSs, governs the allocated computational resources and the output fidelity. Here, we characterize the fidelity for the quantum approximate optimization algorithm by the expectation value of the cost function that it seeks to minimize and find that it follows a scaling law $\mathscr{F}$(ln $\mathcal{χ}$/N), where N is the number of qubits. With ln $\mathcal{χ}$ amounting to the entanglement that a MPS can encode, we show that the relevant variable for investigating the fidelity is the entanglement per qubit. Importantly, our results calibrate the classical computational power required to achieve the desired fidelity and benchmark the performance of quantum hardware in a realistic setup. For instance, we quantify the hardness of performing better classically than a noisy superconducting quantum processor by readily matching its output to the scaling function. Moreover, we relate the global fidelity to that of individual operations and establish its relationship with $\mathcal{χ}$ and N. We sharpen the requirements for noisy quantum computers to outperform classical techniques at running a quantum optimization algorithm in speed, size, and fidelity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Design optimization of integrated cooling inserts in modular Fischer-Tropsch reactors

Sustainable production of liquid fuels and feedstocks from atmospheric CO 2 through carbon recycling technologies is necessary to broaden decarbonization efforts and further reduce global emissions. Fischer–Tropsch (FT) reactors can address this challenge by providing storable, high-value liquid hydrocarbon fuels and feedstocks from syngas generated through reductive CO 2 utilization. FT technology, however, is most cost effective at large-scale, fixed-site plants and does not effectively address the smaller, globally distributed CO 2 point sources. Alternatively, smaller, modular reactors can be composed together to the specific scale of the emission source, yielding a flexible solution that enables more widespread deployment. In these modular reactors, thermal management using a finned cooling insert embedded within the catalyst matrix is critical to maintaining the performance and viability. Thus, in this work, topology optimization is used to determine the cooling insert geometry that maximizes reactor productivity while preventing auto-thermal runaway. Optimal designs are generated for varying number of constituent fins and over a range of maximum operating temperatures. Constraints including minimum feature length-scales and prescribed cooling insert material are imposed on the designs to enhance manufacturability. The impact of design features such as insert tapering and increased length scale hierarchy is automatically revealed by the systematic design framework employed. Here, this approach thus generates novel optimal geometries while automating, accelerating, and enhancing the design process compared to traditional heuristic approaches for cooling insert design in modular FT reactors.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

Gauge-invariant renormalization of four-quark operators

We study the renormalization of four-quark operators in one-loop perturbation theory. We employ a coordinate-space gauge-invariant renormalization scheme (GIRS), which can be advantageous compared to other schemes, especially in nonperturbative lattice investigations. From our perturbative calculations, we extract the conversion factors between GIRS and the modified minimal subtraction scheme ( MS ¯ ) at the next-to-leading order. As a by-product, we also obtain the relevant anomalous dimensions in the GIRS scheme. A formidable issue in the study of the four-quark operators is that operators with different Dirac matrices mix among themselves upon renormalization. We focus on both parity-conserving and parity-violating four-quark operators, which change flavor numbers by two units ( Δ F = 2 ). The extraction of the conversion factors entails the calculation of two-point Green’s functions involving products of two four-quark operators, as well as three-point Green’s functions with one four-quark and two bilinear operators. The significance of our results lies in their potential to refine our understanding of QCD phenomena, offering insights into the precision of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and shedding light on the nonperturbative treatment of complex mixing patterns associated with four-quark operators. Published by the American Physical Society 2024

Constantinou, M. (ORCID:0000000269881745)↗
DOE OSTI2023

Source Characterization of Volatile Organic Compounds at Carlsbad Caverns National Park

Carlsbad Caverns National Park (CAVE), located in southeastern New Mexico, experiences elevated ground-level ozone (O 3 ) exceeding the National Ambient Air Quality Standard (NAAQS) of 70 ppbv. It is situated adjacent to the Permian Basin, one of the largest oil and gas (O&G) producing regions in the US. In 2019, the Carlsbad Caverns Air Quality Study (CarCavAQS) was conducted to examine impacts of different sources on ozone precursors, including nitrogen oxides (NO x ) and volatile organic compounds (VOCs). Here, we use positive matrix factorization (PMF) analysis of speciated VOCs to characterize VOC sources at CAVE during the study. Seven factors were identified. Three factors composed largely of alkanes and aromatics with different lifetimes were attributed to O&G development and production activities. VOCs in these factors were typical of those emitted by O&G operations. Associated residence time analyses (RTA) indicated their contributions increased in the park during periods of transport from the Permian Basin. These O&G factors were the largest contributor to VOC reactivity with hydroxyl radicals (62%). Two PMF factors were rich in photochemically generated secondary VOCs; one factor contained species with shorter atmospheric lifetimes and one with species with longer lifetimes. RTA of the secondary factors suggested impacts of O&G emissions from regions farther upwind, such as Eagle Ford Shale and Barnett Shale formations. The last two factors were attributed to alkenes likely emitted from vehicles or other combustion sources in the Permian Basin and regional background VOCs, respectively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Source characterization of volatile organic compounds at Carlsbad Caverns National Park

Carlsbad Caverns National Park (CAVE), located in southeastern New Mexico, experiences elevated ground-level ozone (O 3 ) exceeding the National Ambient Air Quality Standard (NAAQS) of 70 ppbv. It is situated adjacent to the Permian Basin, one of the largest oil and gas (O&G) producing regions in the US. In 2019, the Carlsbad Caverns Air Quality Study (CarCavAQS) was conducted to examine impacts of different sources on ozone precursors, including nitrogen oxides (NO x ) and volatile organic compounds (VOCs). Here, we use positive matrix factorization (PMF) analysis of speciated VOCs to characterize VOC sources at CAVE during the study. Seven factors were identified. Three factors composed largely of alkanes and aromatics with different lifetimes were attributed to O&G development and production activities. VOCs in these factors were typical of those emitted by O&G operations. Associated residence time analyses (RTA) indicated their contributions increased in the park during periods of transport from the Permian Basin. These O&G factors were the largest contributor to VOC reactivity with hydroxyl radicals (62%). Two PMF factors were rich in photochemically generated secondary VOCs; one factor contained species with shorter atmospheric lifetimes and one with species with longer lifetimes. RTA of the secondary factors suggested impacts of O&G emissions from regions farther upwind, such as Eagle Ford Shale and Barnett Shale formations. The last two factors were attributed to alkenes likely emitted from vehicles or other combustion sources in the Permian Basin and regional background VOCs, respectively. Implications: Carlsbad Caverns National Park experiences ground-level ozone exceeding the National Ambient Air Quality Standard. Volatile organic compounds are critical precursors to ozone formation. Measurements in the Park identify oil and gas production and development activities as the major contributors to volatile organic compounds. Emissions from the adjacent Permian Basin contributed to increases in primary species that enhanced local ozone formation. Observations of photochemically generated compounds indicate that ozone was also transported from shale formations and basins farther upwind. Therefore, emission reductions of volatile organic compounds from oil and gas activities are important for mitigating elevated O 3 in the region.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

3D TRISO particle-explicit compact meshing

The TRI-structural ISOtropic (TRISO) layered fuel particle is a robust nuclear fuel form offering enhanced safety and performance for advanced reactor concepts, including high-temperature gas-cooled reactors and other Generation IV designs. These poppy-seed-sized particles are embedded in a graphite matrix to form fuel elements that must withstand elevated temperatures and high burn-up levels. The heterogeneous nature of these fuel elements — comprising thousands of randomly distributed TRISO particles — produces complex stress fields and thermal gradients that one- and two-dimensional models cannot accurately capture. While three-dimensional modeling has improved predictions of dimensional changes, internal pressure buildup, and fission product transport under irradiation, current approaches rely on homogenized material properties that are known to have considerable divergence from experimental observations. This work presents a methodology for optimized random packing of TRISO fuel compacts and full three-dimensional mesh generation within the BISON fuel performance code, with each particle coating layer individually discretized. The resulting mesh was demonstrated through heat conduction simulations under representative in-reactor operating conditions, showing strong agreement with expected behavior. This capability enables detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating layer failures — all of which directly govern fuel performance and safety margins.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

2025 EIC-France Workshop: Physics Highlights and Perspectives

This document presents a synthesis of the theory contributions and discussions from the 2nd EIC-France Workshop, held at IJCLab (Orsay) on 1-3 December 2025. The workshop brought together members of the French hadron-physics community to review recent theoretical developments relevant to the future Electron-Ion Collider (EIC) and to coordinate national efforts in preparation for its early physics program. The report first summarizes the collider's initial running conditions and luminosity performance, as outlined in the EIC Early Science Matrix. It then provides concise overviews of the theoretical presentations on inclusive, semi-inclusive, exclusive, heavy-flavor, and small-x physics. Based on these discussions, two measurements emerged as especially well suited for early EIC operation and strongly aligned with areas of established French expertise: inclusive diffraction and inclusive quarkonium production. These channels offer clean signatures, robust theoretical interpretability, and direct sensitivity to fundamental QCD phenomena such as gluon saturation, heavy-quark dynamics, and the small-x structure of hadrons and nuclei. In addition, the workshop identified longer-term physics opportunities that will benefit from the full capabilities of the EIC after its ramp-up phase. These include accessing the three-dimensional structure of the pion through the Sullivan process and a broader program of exclusive three-body final states, both of which represent high-impact avenues for exploring hadronic structure and non-perturbative QCD. Together, the elements summarized in this report provide a coherent overview of the strategic priorities and scientific ambitions shaping the French community's contribution to the EIC physics program.

FOS: Physical sciences↗
DOE OSTI2022

Understanding Fission Gas Bubble Distribution and Zirconium Redistribution in Neutron-irradiated U-Zr Metallic Fuel Using Machine Learning

U-10wt.% Zr (U-10Zr) based metallic fuel is the leading candidate for next-generation sodium cooled fast reactor in United States. Currently, Idaho National Laboratory (INL) has been the leading national laboratory for research, development, and demonstration (RD&D) on metallic fuel. Advanced post-irradiation characterization will help to understand fuel microstructure and property change during irradiation, benefiting fuel qualification for commercial application. Characterization capabilities ranging from sub-nanometer to micrometer, such as scanning electron microscopy (SEM), focused ion beam (FIB) sampling, transmission electron microscopy (TEM) characterization, and local thermal conductivity microscopy (TCM), have been utilized recently on irradiated U-10Zr fuel samples to gain a better understanding of nuclear fuel microstructure and property evolution inside a reactor. The FIB/SEM coupled with energy dispersive X-ray spectroscopy (EDS) can capture the essential information to achieve better understanding of fuel behaviors. Inside a nuclear reactor, the phase and microstructure of U-10Zr is constantly changing under neutron bombardment. For example, the gaseous fission product atoms have a limited solubility inside fuel matrix and tend to precipitate out in bubble form, which not only contribute to fuel thermal conductivity degradation but also provide a shortcut for movement of fission products, i.e. lanthanides. The resultant deposition of lanthanides at the cladding inner surface will potentially trigger a chemical reaction/interaction between nuclear fuel and cladding at reactor operational conditions, threatening fuel integrity and safety. FIB/SEM coupled with EDS can provide the fission bubble information as well as probe into phase separation or Zr redistribution, which is fundamental to predict the fuel performance. With high velocity image data generating method, such as FIB/SEM, an automatic way to extract the microstructural information quantitively can better serve the needs from post irradiation characterization. A trained machine learning model, named Decision Tree, is employed to generate a bubble classifier and to categorize bubbles into three categories: isolated bubble, connected without lanthanides, and connected with lanthanides bubbles[3]. This work presents a showcase of this approach on six regions of a fuel cross-section along the radial temperature gradient. We obtained distributions of bubble categories and porosity rates along the six regions. Moreover, a secondary phase U-Zr2 was determined and found on regions 5 and 6. The secondary phase fraction was increasing from 15.61% in region 5 to 34.79% in region 6 based on this approach . This quantitative data offers insights into the lanthanide migration and potentially thermal conductivity degradation. This information from machine learning will be fed into fuel design code for better prediction of fuel performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of φ $-$functions of matrices via quadrature

Here, in this article, we propose an algorithm for approximating the action of φ $-$ functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the φ $-$ functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable, Infiltration-Free Ceramic Matrix Composite (SIF-CMC) manufacturing for Molten Salt Receiver: Investigation of particle-loaded preceramic resin

Due to their unique combination of high temperature, corrosion resistance, and toughness, Ceramic Matrix Composites (CMC) are the optimal materials to be used in the next generation of Concentrated Solar Power (CSP), which will operate at working temperatures up to 800 °C. However, today, CMC is too costly to be used in CSP applications due to its complex manufacturing process based on repeated infiltration-pyrolysis cycles. To solve this issue, PARC is developing a scalable, infiltration-free method (SIF) to manufacture CMC, which can reduce the production cost, increase batch consistency, and leverage all of the intrinsic advantages of current CMCs. The key to the SIF method is using a flowable preceramic resin with high loading of functional components. The formulation impregnates the fiber during curing and leads to high-density, low-shrinkage parts upon pyrolysis. In this paper, we demonstrate a proof-of-concept of the SIF process and report the relationships between key process parameters in the manufacturing process: functional material loading in the resin vs. resin’s flowability and morphology changes upon pyrolysis.

ceramic matrix composite, concentrated solar power↗
DOE OSTI2026

Absorber Clamp for Microcalorimeter Decay Energy Spectrometry

Microcalorimeter Decay Energy Spectrometry (DES) is of interest to nuclear safeguards due to its ability to provide high precision isotopic compositions of nanogram-to microgram-scale samples of Pu and U and related daughter products. The DES method is able to record decay energy of each alpha-decay event in a sample that is embedded in a metal matrix (absorber) and thermally linked to a microcalorimeter detector. This work optimizes the DES technique used to thermally link the absorber and microcalorimeter detector element to allow for more rapid assembly and to increase detector performance and operating life. Optimized attachment methods are crucial for enhancing the viability of DES in high-sample-throughput facilities, such as those that support international nuclear safeguards measurements. Here, in this study, we designed and implemented a pressure-based absorber clamp and evaluated the performance of this new attachment method relative to pressed indium bond attachment. Results using the absorber clamp demonstrate a streamlined detector assembly procedure that minimizes accidental damage to detectors, as well as increasing detector pulse speeds by 57%. Spectral comparison shows the clamp preserves detector performance relative to indium attachment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Fuel performance analysis of fully-resolved TRISO compact

The TRi-structural ISOtropic (TRISO) fuel multilayered coating structure offers multiple barriers to fission product release, enhancing safety and performance. The heterogeneous nature of TRISO fuel compacts, comprising thousands of randomly distributed coated fuel particles embedded in a graphite matrix, creates intricate stress fields and thermal gradients that cannot be accurately modeled using simplified one-dimensional or homogenized approaches. Consequently, three-dimensional modeling enables the prediction of fuel compact dimensional changes, internal pressure buildup, and fission product transport pathways under diverse irradiation and thermal conditions. This capability facilitates detailed analysis of particle-to-particle interactions, matrix cracking mechanisms, and the statistical distribution of coating failures, which directly impact fuel performance and safety margins. This capability is particularly critical for advanced reactors, such as high-temperature gas-cooled reactors and other Generation IV reactor designs where TRISO fuel operates at elevated temperatures and burn-up levels. This work introduces a novel method to generate an optimized packing of TRISO compacts and a complete 3D mesh with random distribution of TRISO particles, which are discretized into each coating component layer.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Measurement of Fission Product Concentration Profiles in AGR-3/4 TRISO Fuel Graphitic Matrix and Nuclear Graphites

The third Advanced Gas Reactor (AGR) irradiation experiment, AGR-3/4, was designed to investigate the migration of fission products in fuel compact graphitic matrix and reactor graphite components. Using destructive methods, radial fission product concentration profiles were measured for gamma-emitting fission products (e.g., Ag-110m, Cs-134, and Eu-154) and beta-emitting Sr-90 in irradiated graphitic and graphite components from six different AGR-3/4 irradiation capsules. These new measured concentration profiles can now be compared to non-destructive measurements and fission product transport simulations and will be used to derive new diffusivities and sorptivities to support refinement of fission product transport models and high-temperature gas-cooled reactor (HTGR) source-term analyses. Each capsule in the AGR-3/4 experiment had four fuel compacts in the middle of two concentric rings of graphitic matrix material, PCEA graphite, or IG-110 graphite. In addition to the approximately 1898 tristructural isotropic (TRISO) coated particles in each compact, there were 20 designed to fail (DTF) particles coated only in pyrocarbon so that they released fission products into the surrounding cylindrical rings of carbonaceous materials. Destructive sampling of the rings involved machining/milling material from around the circumference of the rings, collecting that material, and performing radiochemical analyses on it. Milling operations were performed in multiple steps or segments, and each segment was generally 0.508 mm (0.020 in) thick. Knowing the radial position at which each segment was milled, the volume of the milled material at each segment, and the fission product content in each segment, the radial fission product concentrations were constructed for select isotopes in each ring. Ag-110m profiles had the most variation. Some profiles were peaked at an inner or outer surface. Some were peaked at the middle of the ring wall thickness. Some increased radially outward, and some decreased radially outward. These types of variations and the fact that the measured profiles do not generally compare favorably with the transport model employed for AGR-3/4 may adversely impact the ability to extract reasonable transport parameters for this isotope. In many cases, the Cs-134 profiles decreased somewhat linearly in the outward radial direction, and in cursory comparisons, the shapes of these profiles appeared similar to those from model predictions. The step changes in concentration across the inner-outer ring gap were generally consistent with the model predictions as well. In some cases, there were local maxima in concentration at the outer surface of the rings. This suggests that fission products could have transported in the small gaps between the inner ring and the outer ring and between the outer ring and the sink ring such that some portion of a given fission product can bypass diffusion through the ring itself. The analysis of the small nubs on the outer surfaces of some of the outer rings revealed fission product concentrations in the nubs that were often higher than in the outermost segments of the rings. This further supports the hypothesis that short-circuit, gap transport occurred, causing relatively high surface concentrations on the outer surfaces of the rings. Eu-154 and Sr-90 profiles tend to have very similar shapes, suggesting that they transport via the same mechanisms. The observed profiles were indicative of a transport process where the isotopes are sorbed on the inner surface of the ring, but diffusion into the ring from that surface is quite slow. Some elevated concentrations of Sr-90 (relative to Eu-154) on the outer surface of a ring suggested that rapid, gas-gap transport of gaseous precursor Kr-90 and volatile Rb-90 could have occurred prior to their decaying to Sr-90. Overall, the Eu 154 and Sr-90 profiles were still very similar, which indicates that the transport of short-lived Sr-90 precursors is not a major effect. In some capsules, the qualitative Sr-90 behavior across the ring gaps was consistent with the model (using the available legacy Sr-90 transport parameters), but in other capsules the model was inconsistent with the measurements and seems to underestimate the amount of Sr-90 in the outer rings. The total ring Sr-90 inventories were estimated for all the rings that were subject to physical sampling. These results will be used to adjust the predicted particle and/or compact releases used in the AGR-3/4 fission product transport model. Given the different irradiation temperatures among the capsules and the rings, it was not possible to discern fundamental differences in the transport of isotopes within the different carbon materials, i.e., graphitic matrix, IG-110, or PCEA. It may be possible to do this in the course of determining transport from the concentration profiles in future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Source apportionment of airborne volatile organic compounds near unconventional oil and gas development

Oil and natural gas (ONG) extraction emits volatile organic compounds (VOCs). Certain VOCs are identified as hazardous air pollutants (HAPS) while others contribute to ozone formation. This study examines the impact of ONG operations on VOC levels during the development of multi-well ONG pads in suburban Broomfield, Colorado. From October 2018 to December 2020, weekly VOC measurements were taken at 18 sites across the area. These included spots near well pads, in adjacent neighborhoods, and at a background site, covering various stages of well pad development including drilling, hydraulic fracturing, flowback, and production. Analysis using Positive Matrix Factorization (PMF) identified six factors, including combustion, background/biogenic sources, light and complex alkanes, drilling activities, and ONG acetylene. Factors linked to local ONG activities exhibited clear temporal and spatial correlations with Broomfield well development. Benzene source analysis revealed distinct contribution gradients, with ONG-related sources notably influencing areas near the well pads, particularly in pre-production. ONG-related weekly benzene contributions varied from 9% to 63% at a community background site and 18% to 89% in a neighborhood close to a well pad.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}$ 2 from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the 𝑥-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}$ 2 moment of the twist-3 PDF 𝑔 𝑇 ⁡(𝑥) for the first time in the $\overline{MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing 𝑎 =0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta 𝑃 𝑧 ={0,0.25,1.02,1.53} GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for 𝑔 𝑇 ⁡(𝑥), we obtain $\tilde{d}$$^{u-d}_2$⁡(2 GeV) =0.0024⁢(46) at next-to-leading order in $\overline{MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the 𝑥-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region 𝑥 ∈[0.25,0.75]. The end-point regions are then parametrized, combined with the LaMET prediction at moderate 𝑥, and fitted to the short-distance matrix elements in coordinate space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗