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DOE OSTI2015

Partonic transverse distributions of up and down quarks

The quark-gluon dynamics manifests itself in a set of non-perturbative functions describing all possible spin-spin and spin-orbit correlations. The Transverse Momentum Dependent parton distributions (TMDs) and Generalized Parton Distributions (GPDs) carry information not only on the longitudinal but also on the transverse momentum and position of partons, providing rich and direct information on the orbital motion of quarks. Single and Dihadron semi-inclusive and hard exclusive production, both in current and target fragmentation regions, provide a variety of spin and azimuthal angle dependent observables, sensitive to the dynamics of quark-gluon interactions. Studies of the 3D PDFs are currently driving the upgrades of several existing facilities (JLab, COMPASS and RHIC), and the design and construction of new facilities worldwide (EIC, FAIR, and JPARC). In this talk, we present an overview of the current status and some future measurements of the orbital structure of nucleons at Jefferson Lab.

Avagyan, Harutyun↗

DOE OSTI2015

Studies of transverse momentum dependent parton distributions and Bessel weighting

In this paper we present a new technique for analysis of transverse momentum dependent parton distribution functions, based on the Bessel weighting formalism. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. Using a fully differential cross section for the process, the effect of four momentum conservation is analyzed using various input models for transverse momentum distributions and fragmentation functions. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy/Q 2 . We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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

Exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions for extracting generalized parton distributions

We show that exclusive production of a pair of high transverse momentum photons in pion-nucleon collisions can be systematically studied in QCD factorization approach if the photon’s transverse momentum q T with respect to the colliding pion is much greater than Λ QCD . We demonstrate that the leading power non-perturbative contributions to the scattering amplitudes of this exclusive process are process-independent and can be systematically factorized into universal pion’s distribution amplitudes (DAs) and nucleon’s generalized parton distributions (GPDs), which are convoluted with corresponding infrared safe and perturbatively calculable short-distance hard parts. The correction to this factorized expression is suppressed by powers of 1/q T . We demonstrate quantitatively that this new type of exclusive processes is not only complementary to existing processes for extracting GPDs, but also capable of providing an enhanced sensitivity to the dependence of both DAs and GPDs on the active parton’s momentum fraction x. We also introduce additional, but the same type of exclusive observables to enhance our capability to explore GPDs, in particular, their x-dependence.

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 OSTI2015

Quasi-parton distribution functions: A study in the diquark spectator model

A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum P z is very large. Since taking the P z → ∞ limit is not feasible in lattice simulations, it is essential to provide guidance for what values of P z the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f 1 , helicity distribution g 1 , and transversity distribution h 1 ). We find that, for intermediate parton momentum fractions x, quasi-PDFs are good approximations to standard PDFs (within 20–30) when P z ≳ 1.5–2 GeV. On the other hand, for large x ~ 1 much larger P z > 4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.

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 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

Complete definition of 𝑁 →Δ transition generalized parton distributions

We revisit the definition of the leading-twist chiral-even generalized parton distributions (GPDs) for 𝑁 →Δ baryon transitions. We identify and address deficiencies in previous definitions of the transition GPDs inspired by the transition form factors of the vector and axial vector currents. Through systematic analysis of all possible covariant structures, respecting discrete symmetries and the baryon spinor equations of motion, we derive complete sets of independent structures for the transition matrix elements of the vector and axial vector partonic operators. They contain additional structures proportional to the light-cone vector, corresponding to transition GPDs of vanishing first moment, which were not included in previous parametrizations. Their presence is confirmed independently by the light-front multipole expansion and the cross-channel SO(3) partial-wave analysis of the transition matrix elements. Our analysis provides a complete definition of the 𝑁 →Δ transition GPDs for use in theoretical and phenomenological studies.

baryons↗

DOE OSTI2024

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ( γ γ ) and a massive pair of leptons ( ℓ + ℓ − ) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction x dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Parton distributions from boosted fields in the Coulomb gauge

We propose a new method to calculate parton distribution functions (PDFs) from lattice correlations of boosted quarks and gluons in the Coulomb gauge. Compared to the widely used gauge-invariant Wilson-line operators, these correlations greatly simplify the renormalization thanks to the absence of linear power divergence. Additionally, they enable access to larger off-axis momenta under preserved 3D rotational symmetry, as well as enhanced long-range precision that facilitates the Fourier transform. We verify the factorization formula that relates this new observable to the quark PDF at one-loop order in perturbation theory. Moreover, through a lattice calculation of the pion valence quark PDF, we demonstrate the aforementioned advantage and features of the Coulomb gauge correlation and show that it yields consistent results with the gauge-invariant method. This opens the door to a more efficient way to calculate parton physics on the lattice.

Baryons↗

DOE OSTI2025

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗

DOE OSTI2018

Fractional Quantum Hall Effect at ν = 2 + 6 / 13 : The Parton Paradigm for the Second Landau Level

Here, the unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at ν = 2 + 6/13 offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a “ $\bar{3}$ $\bar{2}$111” parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $\bar{3}$ $\bar{2}$111 state to be a good candidate for the ν = 2 + 6/13 FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. Furthermore, we propose that the “n$\bar{2}$111” family of parton states naturally describes many observed SLL FQHE plateaus.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Parton Distribution Functions from a Light Front Hamiltonian and QCD Evolution for Light Mesons

Here, we obtain the pion and the kaon parton distribution functions from the eigenstates of a light front effective Hamiltonian in the constituent quark-antiquark representation suitable for low-momentum scale applications. By taking these scales as the only free parameters, the valence quark distribution functions of the pion, after QCD evolution, are consistent with the data from the FNAL-E615 experiment. The ratio of the up quark distribution of the kaon to that of the pion also agrees with the CERN-NA3 experiment. Supplemented by known parton distribution functions for the nucleons, we also obtain the cross section consistent with experimental data for the π - nucleus → μ + μ - X Drell-Yan process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Moments of parton distribution functions of the pion from lattice QCD using gradient flow

We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios ⟨𝑥 𝑛−1 ⟩/⟨𝑥⟩ up to 𝑛 = 6, using the gradient flow in lattice quantum chromodynamics (QCD). As a testing ground, we employ SU(3) isosymmetric gauge configurations generated by the OpenLat initiative with a pseudoscalar mass of 𝑚 𝜋 ≃ 411 MeV. Our analysis uses four lattice spacings and a nonperturbatively improved action, enabling full control over the continuum extrapolation, and the limit of vanishing flow time, 𝑡 →0. The flowed ratios exhibit O(𝑎 2 ) scaling across the ensembles, and the continuum-extrapolated results, matched to the $\overline{MS}$ scheme at 𝜇 = 2 GeV using next-to-next-to-leading order matching coefficients, show only mild residual flow-time dependence. The resulting ratios, computed with a relatively small number of configurations, are consistent with phenomenological expectations for the pion’s valence distribution, with statistical uncertainties that are competitive with modern global fits. These findings demonstrate that the gradient flow provides an efficient and systematically improvable method to access partonic quantities from first principles. Future extensions of this work will target lighter pion masses toward the physical point, and applications to nucleon structure such as the proton PDFs and the gluon and sea-quark distributions.

lattice QCD↗

DOE OSTI2025

Fresh look at the nuclear transparency using the generalized parton distributions

Color transparency (CT) is a fundamental phenomenon in QCD in which hadrons produced in high-energy exclusive processes traverse nuclear matter with minimal interactions. Nuclear transparency, which quantifies this attenuation suppression, is a quantity with high sensitivity to CT effects and provides critical insights into QCD dynamics in nuclear environments. In this study, we revisit nuclear transparency using the framework of generalized parton distributions (GPDs). By constructing nuclear GPDs (nGPDs) through the incorporation of nuclear parton distribution functions, we calculate the nuclear transparency 𝑇⁡(𝑄 2 ) for the carbon nucleus as a function of momentum transfer 𝑄 2 considering various definitions and compare the results obtained with available experimental data. Our finding highlights the importance of choosing a physically motivated definition of nuclear transparency. Moreover, we emphasize that a more reliable determination of nGPDs requires a dedicated global analysis incorporating nuclear data. Such an approach is essential for improving the theoretical understanding of CT and for achieving consistency with experimental observations in the high-𝑄 2 regime.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

CT14 intrinsic charm parton distribution functions from CTEQ-TEA global analysis

We investigate the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon, theoretical issues arising in its interpretation, and its potential impact on LHC scattering processes. The “fitted charm” PDF obtained in various QCD analyses contains a process-dependent component that is partly traced to power-suppressed radiative contributions in DIS and is generally different at the LHC. We discuss separation of the universal component of the nonperturbative charm from the rest of the radiative contributions and estimate its magnitude in the CT14 global QCD analysis at the next-to-next-to leading order in the QCD coupling strength, including the latest experimental data from HERA and the Large Hadron Collider. Models for the nonperturbative charm PDF are examined as a function of the charm quark mass and other parameters. The prospects for testing these models in the associated production of a Z boson and a charm jet at the LHC are studied under realistic assumptions, including effects of the final-state parton showering.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

Abstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, theheavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.

Physics↗