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DOE OSTI2020

Exploring Hadron Structure with GPDs at EIC: New Topics in Theory, Experiment, Interpretation

Exploring hadron structure with generalized parton distributions (GPDs) and related concepts is an essential part of the physics program of the planned Electron-Ion Collider (EIC). Here, we discuss new topics in GPD physics (theory, experiment, interpretation) that have emerged in the last years and could be included in the EIC program. This includes: (a) D-term and QCD forces in the nucleon; (b) Transversity GPDs in pseudoscalar meson production and high-mass pair production; (c) Pion and kaon form factors and GPDs; (d) Transition distribution amplitudes and backward meson production; (e) Neutron GPDs and nuclear modifications; (f) Nuclear GPDs and quark/gluon imaging of nuclei; (g) Twist-3 GPDs and quark-gluon correlations; (h) Wigner functions and potential observables. We also comment on future theoretical developments needed for the GPD program at EIC and emerging connections with other areas of nuclear physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD

We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.

Electron-ion collisions↗

DOE OSTI2026

Rapidity-dependent spin decomposition of the nucleon

We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4⁢𝜂 2 ⁢𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ⁢𝑦 = ln⁡[(1+𝜂)/(1−𝜂)] = 2 artanh⁡(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).

Gauge-gravity dualities↗

DOE OSTI2025

String-based axial and helicity-flip GPDs: A comparison to lattice QCD

We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.

Gauge-gravity dualities↗

DOE OSTI2026

Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators

We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution up to fifth order ⟨𝑥 4 ⟩ and for the skewness range [−0.33, 0] using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing 𝑎 = 0.04 fm and valence pion mass 300 MeV, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV 2 . We employ ratio-scheme renormalization and next-to-leading logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Tensor-polarized parton density in the $N → Δ$ transition

The generalized parton distributions for transitions between baryon states with different masses have a forward limit in which they behave as parton densities (light-front momentum transfer Δ + , Δ T = 0, energy transfer Δ - ≠ 0). These "transition parton densities" can realize spin/isospin quantum numbers not accessible in the ground-state nucleon. The N → Δ transition gives rise to a new parton density proportional to the 1/2 → 3/2 spin transition tensor. Its properties are derived, and its magnitude is estimated in the chiral quark-soliton model based on the large-N c limit of QCD.

Delta isobar↗

DOE OSTI2025

Probing hard/soft factorization via beam-spin asymmetry in exclusive pion electroproduction from the proton

Deep exclusive meson production (DEMP) reactions, such as $p(\vec{e}, e' π^+)n$, provide opportunities to study the three-dimensional structure of the nucleon through differential cross section and beam- and target-spin asymmetry measurements. This work aims to probe the onset of the hard/soft factorization regime through the exclusive $p(\vec{e}, e' π^+)n$ reaction, as measured in the KaonLT experiment at Jefferson Lab Hall C. A 10.6 GeV longitudinally polarized electron beam was incident on an unpolarized liquid hydrogen target, and the scattered electron and produced meson were detected in two magnetic focusing spectrometers, enabling precision cross section measurements. The cross section ratio $σ_{LT'}/σ_0$ was extracted from the beam-spin asymmetry $A_{LU}$. The t -dependence of $σ_{LT'}/σ_0$ was determined at fixed $Q^2$ and $x_B$ over a range of kinematics from 2 < $Q^2$ < 6 GeV$^2$ above the resonance region ($W$ > 2 GeV). Furthermore, these data are combined with recent results from CLAS/CLAS12 to determine the $Q^2$-dependence of at two $(x_B, t)$ settings. This was fairly flat, with $Q^2$ not having a measurable effect on the value of in the range explored. Results are compared to predictions from the generalized parton distribution (GPD) formalism, which relies explicitly on hard/soft factorization, and Regge formalism. The Regge models better predict $σ_{LT'}/σ_0$, which suggests that the factorization regime is not yet reached.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Transverse orbital angular momentum in the proton

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution g T . We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, k T , of the generalized transverse momentum-dependent distribution F 12 , or alternatively in terms of the twist-three generalized parton distributions H 2T and $\tilde{E}$ 2T .

Lorentz invariance relations↗

DOE OSTI2024

Double distributions and pseudodistributions

We describe the approach to lattice extraction of generalized parton distributions (GPDs) that is based on the use of the double distribution (DD) formalism within the pseudodistribution framework. The advantage of using DDs is that GPDs obtained in this way have the mandatory polynomiality property, a nontrivial correlation between x and ξ dependences of GPDs. Another advantage of using DDs is that the D -term appears as an independent entity in the DD formalism rather than a part of GPDs H and E . We relate the ξ dependence of GPDs to the width of the α profiles of the corresponding DDs and discuss strategies for fitting lattice-extracted pseudodistributions by DDs. The approach described in the present paper may be used in ongoing and future lattice extractions of GPDs. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Exploring the 3D nucleon structure with CLAS and CLAS12 at JLAB

Exploring the 3 dimensional structure of the nucleon can help to understand several fundamental questions of nature, such as the origin of the nucleon spin and the charge and density distributions inside the nucleon. In QCD, the 3-dimensional structure of the nucleon is described by Wigner functions. However, experimentally momentum and coordinate space have to be assessed independently. The momentum distribution can be accessed by transverse momentum dependent distribution functions (TMDs) measured in semi-inclusive deep inelastic scattering (SIDIS) or Drell-Yan processes while the distribution in transverse coordinate and longitudinal momentum space is described by generalized parton distributions (GPDs) which can be accessed for example by deeply virtual Compton scattering (DVCS) and hard exclusive meson production (DVMP). Based on the high quality data of CLAS and the recently upgraded CLAS12 detector at Jefferson Laboratory (JLAB), a detailed study of these distribution functions is being performed. With the new CLAS12 data, multidimensional, high precision studies in an extended kinematic range become possible for the first time. The talk will present the results of recent SIDIS, DVCS and DVMP studies with CLAS and CLAS12 and their impact on the understanding of the 3D nucleon structure.

Diehl, Stefan↗

DOE OSTI2022

Twist-three cross-sections in deeply virtual Compton scattering

We study the deeply virtual Compton scattering process with both twist-two and twist-three Compton form factors and present our cross-sections formulas with all polarization configurations. While the twist-three contributions are generally assumed to be negligible in the literature due to the kinematical suppression, we compare them with the twist-two ones at typical JLab 6 GeV and 12 GeV kinematics as well as EIC kinematics and show their kinematical suppression explicitly, justifying the leading-twist approximation made in the literature. In addition, we also estimate the twist-three Compton form factors using Wandzura-Wilczek relations and inputs of twist-two generalized parton distributions based on a reggeized spectator model. With those estimated Compton form factors, we analyze the kinematical behavior of twist-two and twist-three cross-sections in a wide range of kinematics, and discuss the optimal regions for separating the leading-twist effects from the higher-twist ones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Exploring the gravitational structure of the proton with the dilepton final state using the CLAS12 detector at Jefferson Lab

The Gravitational Form Factors (GFFs) give access to the internal distributions of mass, pressure and shear force inside the proton. They were considered experimentally unmeasurable for decades due to the very weak gravitational interaction [1]. However, the Generalized Parton Distributions (GPDs), which describe the correlations between the longitudinal momentum and the transverse position of the partons inside the nucleon, have lately been related to the GFFs. For the first time, this relation gives the opportunity to extract GFFs experimentally. In this talk, I will present two ways to access GFFs using data taken in 2018 by the CLAS12 detector with a 10.6 GeV electron beam impinging on a liquid-hydrogen target. First, I will present the first measurement of the Timelike Compton Scattering reaction (the hard photoproduction of a lepton pair), that gives access to the quark GFFs via the angular asymmetry of the electron/positron pair [2]. I will then present the current effort to extract the near-threshold J/? photoproduction cross section using the same dataset. This later measurement is expected to provide direct insight on the gluons GFFs of the proton. [1] H. PAGELS. Energy-Momentum Structure Form Factors of Particles. Phys.Rev. 144 (1966) 1250-1260 [2] P. Chatagnon. First Measurement of Timelike Compton Scattering. Phys.Rev.Lett. 127 (2021) 26, 262501

Chatagnon, Pierre↗

DOE OSTI2021

Neutral Pion Electroproduction Cross sections from 12 GeV Jefferson Lab for x B > 0 . 3

Nuclear physics aims at understanding structure of the building blocks of the atom, the protons and neutrons in terms of their constituents, the quarks and gluons. Traditionally, this was accomplished through studies of their static properties and the underlying one-dimensional quark and gluon momentum distributions. Over the last few decades, realization has grown that the true study of the proton dynamical structure has to come from more exclusive reactions. These deep exclusive processes describe a subset of unique inelastic processes in which all particles in their final state are detected. Such processes can allow access to Generalized Parton Distributions, or GPDs, a conceptual mechanism that lies at the root of three-dimensional spatial imaging of the proton?s quark-gluon substructure. In particular, photon electroproduction as well as meson electroproduction are two kinds of deep inelastic processes that can allow access to GPDs. Deeply Virtual Compton Scattering (DVCS) is a type of deep inelastic process, and is known as one of the cleanest ways to access GPDs.

Ali, Salina↗

DOE OSTI2023

Neutron Magnetic Form Factor GNM Measurement at High Q2 with CLAS12

The neutron magnetic form factor, GnM , is a fundamental quantity that describes how magnetic properties are distributed within a neutron. This measurement provides insights into the internal structure of the neutron. Furthermore, by measuring GnM alongside three other form factors (GnE , GpE , GpM ), we can test the predictions of Quantum Chromodynamics (QCD), which is the fundamental theory governing the strong force that binds quarks and gluons. Additionally, these measurements play a significant role in constraining Generalized Parton Distributions (GPDs) and contribute to determining the angular momentum of the quarks within nucleons. The GnM was measured using the ratio of quasi-elastic e ? n to e ? p scattering from a deuteron target. The measurement covered a range of four-momentum transfer squared, Q2, from 5 to 12 GeV2, using three different beam energies (10.2, 10.4, and 10.6 GeV). The data is compared with previous measurements and several theoretical models. The preliminary results reveal that Gn M exceeds the predictions of the standard dipole parametrization by 12-20%, based on RG-B pass1 data. It is expected that this deviation from the standard dipole parametrization will diminish as we transition to using RG-B pass2 data, aligning GnM more closely with the dipole form factor. The ongoing RG-B pass2 analysis in CLAS12 holds considerable promise for significant improvement. This enhancement is achievable through collaborative efforts aimed at refining tracking efficiency, momentum correction, calibration, and alignment.

Baashen, Lamya↗

DOE OSTI2020

Theoretical and Phenomenological Studies of the Nucleon Structure in High Energy Reactions

The understanding of the internal structure of the proton and other strongly interacting particles is at the forefront of modern nuclear physics research. Generalized Parton Distribution Functions (GPDs) are a powerful tool to advance the understanding of hadron structure. In addition to the information about the one- dimensional collinear momentum distributions of partons (quarks, anti-quarks, and gluons) known from studies of high energy deep-inelastic reactions, GPDs also carry information on the distribution of partons in the transverse plane, and allow us in this way to access the three-dimensional structure of the nucleon. GPDs can be studied in hard-exclusive reactions and contain also information on the energy-momentum tensor form factors which will allow us to gain insights on quantities like pressure or angular momentum distribution inside the nucleon. The goal of this thesis is to deepen our understanding of the three-dimensional structure of the nucleon. We investigate energy-momentum tensor form factors and densities, and all leading-twist GPDs in the bag model. This quark model provides a consistent theoretical framework to investigate many general concepts that have recently attracted interest, and allows one to study insightful limits like the large-Nc limit, heavy-quark limit or the non-relativistic limit. Another important aspect of this thesis is the discussion of the monopole and quadrupole contributions to the angular momentum density. Finally, the description of pseudoscalar meson production in exclusive processes in terms of GPDs is discussed in the Goloskokov-Kroll model and implemented in the PARTONS framework, a software development project which will provide direct support for experiments at the Jefferson National Lab and the future Electron-Ion Collider.

Tezgin, Kemal↗

DOE OSTI2021

Large-momentum effective theory

Since the parton model was introduced by Feynman more than 50 years ago, much has been learned about the partonic structure of the proton through a large body of high-energy experimental data and dedicated global fits. However, limited progress has been made in calculating partonic observables such as the parton distribution function (PDFs) from the fundamental theory of strong interactions, quantum chromodynamics (QCD). Recently some advocated for a formalism, large-momentum effective theory (LaMET), through which one can extract parton physics from the properties of the proton traveling at a moderate boost factor such as γ ~ 2 – 5 . The key observation behind this approach is that Lorentz symmetry allows the standard formalism of partons in terms of light-front operators to be replaced by an equivalent one with large-momentum states and time-independent operators of a universality class. With LaMET, the PDFs, generalized PDFs or generalized parton distributions, transverse-momentum-dependent PDFs, and light-front wave functions can all be extracted in principle from lattice simulations of QCD (or other nonperturbative methods) through standard effective field theory matching and running. Future lattice QCD calculations with exascale computational facilities could help one to understand the experimental data related to the hadronic structure, including those from the upcoming electron-ion colliders dedicated to exploring the partonic landscape of the proton. In this work, the progress made in the past few years in the development of the LaMET formalism and its applications is reviewed, with an emphasis on a demonstration of its effectiveness from initial lattice QCD simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Models of $J/\varPsi$ photo-production reactions on the nucleon

The J/Ψ photo-production reactions on the nucleon can provide information on the roles of gluons in determining the J/Ψ-nucleon (J/Ψ-N) interactions and the structure of the nucleon. The information on the J/Ψ-N interactions is needed to test lattice QCD (LQCD) calculations and to understand the nucleon resonances such as N*(P c ) recently reported by the LHCb Collaboration. In addition, it is also needed to investigate the production of nuclei with hidden charms and to extract the gluon distributions in nuclei. The main purpose of this article is to review six models of the γ+p→J/Ψ+p reaction which have been and can be applied to analyze the data from Thomas Jefferson National Accelerator Facility (JLab). Here, the formulae for each model are given and used to obtain the results to show the extent to which the available data can be described. The models presented include the Pomeron-exchange model of Donnachie and Landshoff (Pom-DL) and its extensions to include J/Ψ-N potentials extracted from LQCD (Pom-pot) and to also use the constituent quark model (CQM) to account for the quark substructure of J/Ψ (Pom-CQM). The other three models are developed from applying the perturbative QCD approach to calculate the two-gluon exchange using the generalized parton distribution (GPD) of the nucleon (GPD-based), two- and three-gluon exchanges using the parton distribution of the nucleon (2g+3g), and the exchanges of scalar (0 ++ ) and tensor (2 ++ ) glueballs within the holographic formulation (holog). The results of investigating the excitation of the nucleon resonances N*(P c ) in the γ+p→J/Ψ+p reactions are also given. We demonstrate that the differences between these six models can be unambiguously distinguished and the N* can be better studied by using the forthcoming JLab data at large |t| and at energies very near the J/Ψ production threshold. Possible improvements of the considered models are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Higher-order kinematical effects in deeply virtual Compton scattering

We study the deeply virtual Compton scattering cross-section in twist-two generalized parton distribution (GPD) approximation, and show that different choices of light-cone vectors and gauges for the final photon polarization will lead to different higher-order kinematical corrections to the cross-section formula. The choice of light-cone vectors affects kinematic corrections at the twist-three level, accounting for the differences between the cross-section formulas in the literature. On the other hand, kinematical corrections from higher-twist GPDs should eliminate the light-cone dependence at twist three. Those light-cone dependencies are studied systematically at JLab 12 GeV and future EIC kinematics. They serve as the intrinsic systematic uncertainties in extracting the Compton form factors through the cross-section formula. More importantly, they are also necessary for understanding cross-section measurements with higher-twist precision and to reconstruct higher-order Compton form factors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗