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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Kernel methods for evolution of generalized parton distributions

Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The dependence of GPDs on the factorization scale Q 2 allows one to connect hard exclusive processes involving GPDs at disparate energy and momentum scales, which is needed in global analyses of experimental data. Here, in this work, we explore how finite element methods can be used to construct fast and differentiable Q 2 evolution codes for GPDs in momentum space, which can be used in a machine learning framework. We show numerical benchmarks of the methods' accuracy, including a comparison to an existing evolution code from PARTONS/APFEL++, and provide a repository where the code can be accessed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Gaussian processes for inferring parton distributions

The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.

hadronic spectroscopy↗
DOE OSTI2024

Consistency of the pion form factor and unpolarized transverse momentum dependent parton distributions beyond leading twist in the light-front quark model

We investigate the interplay among the pion’s form factor, transverse momentum dependent distributions (TMDs), and parton distribution functions (PDFs) extending our light-front quark model (LFQM) computation based on the Bakamjian-Thomas construction for the two-point function [1,2] to the three-point and four-point functions. Ensuring the four-momentum conservation at the meson-quark vertex from the Bakamjian-Thomas construction, the meson mass is taken consistently as the corresponding invariant meson mass both in the matrix element and the Lorentz factor in our LFQM computation. We achieve the current-component independence in the physical observables such as the pion form factor and delve into the derivation of unpolarized TMDs and PDFs associated with the forward matrix element. We address the challenges posed by twist-4 TMDs and exhibit the fulfillment of the sum rule. Effectively, our LFQM successfully handles the light-front zero modes and offers insights for broader three-point and four-point functions and related observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy

We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and 𝜌-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-𝑥 regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.

Form factors↗
DOE OSTI2022

Impact of jet-production data on the next-to-next-to-leading-order determination of HERAPDF2.0 parton distributions

The HERAPDF2.0 ensemble of parton distribution functions (PDFs) was introduced in 2015. The final stage is presented, a next-to-next-to-leading-order (NNLO) analysis of the HERA data on inclusive deep inelastic ep scattering together with jet data as published by the H1 and ZEUS collaborations. A perturbative QCD fit, simultaneously of $\alpha _s(M_Z^2)$ and the PDFs, was performed with the result $\alpha _s(M_Z^2)= 0.1156 \pm 0.0011~\mathrm{(exp)}~ ^{+0.0001}_{-0.0002}~ \mathrm{(model}$ $\mathrm{+ parameterisation)}~ \pm 0.0029~\mathrm{(scale)}$. The PDF sets of HERAPDF2.0Jets NNLO were determined with separate fits using two fixed values of $\alpha _s(M_Z^2)$, $\alpha _s(M_Z^2)$ = 0.1155 and 0.118, since the latter value was already chosen for the published HERAPDF2.0 NNLO analysis based on HERA inclusive DIS data only. The different sets of PDFs are presented, evaluated and compared. The consistency of the PDFs determined with and without the jet data demonstrates the consistency of HERA inclusive and jet-production cross-section data. The inclusion of the jet data reduced the uncertainty on the gluon PDF. Predictions based on the PDFs of HERAPDF2.0Jets NNLO give an excellent description of the jet-production data used as input.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Generalized parton distributions from the pseudodistribution approach on the lattice

Generalized parton distributions (GPDs) are key quantities for the description of a hadron’s three-dimensional structure. They are the current focus of all areas of hadronic physics—phenomenological, experimental and theoretical, including lattice QCD. Synergies between these areas are desirable and essential to achieve precise quantification and understanding of the structure of, particularly, nucleons, as the basic ingredients of matter. In this paper, we investigate, for the first time, the numerical implementation of the pseudodistribution approach for the extraction of zero-skewness GPDs for unpolarized quarks. Pseudodistributions are Euclidean parton correlators computable in lattice QCD that can be perturbatively matched to the light-cone parton distributions of interest. Although they are closely related to the quasidistributions and come from the same lattice-extracted matrix elements, they are, however, subject to different systematic effects. We use the data previously utilized for quasi-GPDs and extend it with other momentum transfers and nucleon boosts, in particular a higher one ( P 3 = 1.67 GeV ) with eightfold larger statistics than the largest one used for quasidistributions ( P 3 = 1.25 GeV ). We renormalize the matrix elements with a ratio scheme and match the resulting Ioffe time distributions to the light cone in coordinate space. The matched distributions are then used to reconstruct the x dependence with a fitting . We investigate some systematic effects related to this procedure, and we also compare the results with the ones obtained in the framework of quasi-GPDs. Our final results involve the invariant four-momentum transfer squared ( − t ) dependence of the flavor nonsinglet ( u − d ) H and E GPDs. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Threshold resummation for computing large-x parton distribution through large-momentum effective theory

Parton distribution functions (PDFs) at large x are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-x through large-momentum P z expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale P z |1 – y| and a pair of heavy-light Sudakov form factors at scale P z . The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-x PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Nucleon form factors and parton distributions in nonlocal chiral effective theory

In this work, we present a review of recent applications of nonlocal chiral effective theory to hadron structure studies. Starting from a nonlocal meson-baryon effective chiral Lagrangian, we show how the introduction of a correlation function representing the finite extent of hadrons regularizes the meson loop integrals and introduces momentum dependence in vertex form factors in a gauge invariant manner. We apply the framework to the calculation of nucleon electromagnetic form factors, unpolarized and polarized parton distributions, as well as transverse momentum dependent distributions and generalized parton distributions. Assuming that the nonlocal behavior is a general property of all interactions, we also discuss the application to the lepton anomalous magnetic moment in nonlocal QED.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Generalized parton distributions through universal moment parameterization: non-zero skewness case

We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs) and deeply virtual Compton scattering (DVCS) measurements. Following the previous work where we parameterize GPDs in terms of their moments, we extend the framework to allow for the global analysis at non-zero skewness. Together with the constraints at zero skewness, we fit GPDs to global DVCS measurements from both the recent JLab and the earlier Hadron-Electron Ring Accelerator (HERA) experiments with two active quark flavors and leading order QCD evolution. With certain choices of empirical constraints, both sea and valence quark distributions are extracted with the combined inputs, and we present the quark distributions in the proton correspondingly. We also discuss how to extend the framework to accommodate more off-forward constraints beyond the small ξ expansion, especially the lattice calculated GPDs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Generalized parton distributions through universal moment parameterization: zero skewness case

We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t-dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Twist-3 partonic distributions from lattice QCD

Twist-3 partonic distributions contain important information that characterizes nucleon’s structure. In this work, we show our lattice exploration of the twist-3 PDFs g_T(x) g T ( x ) , and h_L(x) h L ( x ) . We also present our preliminary results on the twist-3 GPD \tilde{G}_2(x) G ̃ 2 ( x ) . We use the quasi-distribution approach to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that we developed in parallel. We also calculate the twist-2 counterparts of g_T(x) g T ( x ) and h_L(x) h L ( x ) , i.e. g_1(x) g 1 ( x ) , and h_1(x) h 1 ( x ) , and test the Wandzura-Wilczek approximation.

Bhattacharya, Shohini↗
DOE OSTI2025

Kaon gluon parton distribution and momentum fraction from 2+1+1 lattice QCD with high statistics

We present a high-statistics lattice-QCD determination of the kaon gluon parton distribution function and gluon momentum fraction. We use clover valence fermion action to take 1,296,640 kaon-correlator measurements on a highly improved staggered quark ensemble with 𝑎 ≈ 0.12 fm and 310-MeV pion mass generated by the MILC Collaboration. A detailed investigation into the impact of gauge-link smearing on the gluonic matrix elements indicates that five steps of hypercubic smearing offer an effective balance between signal quality and preservation of long-distance physics. We report a nonperturbatively renormalized kaon gluon momentum fraction of Math output error at 𝜇 = 2 GeV in the Math output error scheme. Using reduced pseudo-Ioffe-time-distribution matrix elements and pseudo-parton-distribution-function (PDF) matching, we extract the kaon gluon PDF and compare with the prediction from the Dyson-Schwinger equation and with the pion PDF obtained from the same ensemble.

First-principles calculations↗
DOE OSTI2025

Parton distribution functions from scalar light-front parton gas model

Here, we propose an application of a microcanonical ensemble with light-front kinematics to model the phase-space distribution of relativistic constituents of a bound state. These constituents denoted by partons are treated as classical spin-zero particles confined inside the bound state with inter-parton collisions as their only interaction. The microcanonical molecular dynamics ensemble is applied to obtain the phase-space distribution of such a thermodynamic system. We sample this phase-space distribution using Monte Carlo algorithms to obtain the parton distribution functions (PDFs) in scenarios with 3, 4, and 5 identical partons. In addition PDFs when a selected number of massless partons are mixed with 3 massive partons are also presented.

Microcanonical ensemble↗
DOE OSTI2024

Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb Gauge

Recently, a new method has been proposed to compute parton distributions using boosted correlators fixed in the Coulomb gauge (CG) within the framework of large-momentum effective theory. This approach, which does not involve Wilson lines, could greatly improve the efficiency and precision of lattice quantum chromodynamics calculations. However, concerns remain regarding whether systematic uncertainties from Gribov copies, which correspond to ambiguities in lattice gauge-fixing, are adequately controlled. This work assesses the effects of Gribov copies on Coulomb-gauge-fixed quark correlators. We utilize different strategies for Coulomb-gauge fixing, selecting two different groups of Gribov copies based on lattice gauge configurations. We examine the differences in the resulting spatial quark correlators in both vacuum and pion states. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise, demonstrating that the effect of the Gribov copies can be neglected in practical lattice calculations of quark parton distributions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Evolution of parton distribution functions in the short-distance factorization scheme

Lattice QCD offers the possibility of computing parton distributions from first principles, although not in the usual $\overline{MS}$ factorization scheme. Calculations are therefore matched to $\overline{MS}$ using a perturbative procedure which is the source of significant uncertainty within the currently accessible kinematics. We present the possibility of computing the z 2 evolution of non-singlet pseudo-parton distribution functions within the short factorization scheme in a numerically improvable way. The goal is to have tools to evolve a calculation to a scale where perturbative uncertainties are less pronounced. We compare a numerical extraction of the evolution operator from lattice data to the computation of z 2 dependence in perturbation theory. Finally, we discuss how this numerical work may be extended to address the two-scale problem that arises when the Ioffe time range must be made large to extend the reach of the calculation of the pseudo-PDF to smaller values of the momentum fraction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Twist-3 generalized parton distribution for the proton from basis light-front quantization

We investigate the twist-3 generalized parton distributions (GPDs) for the valence quarks of the proton within the basis light-front quantization (BLFQ) framework. We first solve for the mass spectra and light-front waved functions (LFWFs) in the leading Fock sector using an effective Hamiltonian. Using the LFWFs we then calculate the twist-3 GPDs via the overlap representation. By taking the forward limit, we also get the twist-3 parton distribution functions (PDFs), and discuss their properties. Our prediction for the twist-3 scalar PDF agrees well with the CLAS experimental extractions.

Astronomy & Astrophysics↗
DOE OSTI2026

Gradient Flow for Parton Distribution Functions: First Application to the Pion

Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides ⟨𝑥⟩, face severe challenges from reduced hypercubic symmetry, limiting results to the lowest moments. A recently proposed method resolves these issues using gradient flow. We demonstrate the efficacy of this method by computing ratios of flavor nonsinglet pion PDF moments up to ⟨𝑥 5 ⟩ on four lattice spacings at 𝑚 𝜋 ≃ 411 MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.

Francis, Anthony [National Yang Ming Chiao Tung Un↗