Three-dimensional imaging of hadrons with hard exclusive reactions: advances in experiment, theory, phenomenology, and lattice QCD

TL;DR

This white paper surveys the Generalized Parton Distributions (GPDs) framework as a powerful tool to image hadron structure in three dimensions via hard exclusive reactions like DVCS and DVMP. It compiles advances across theory, lattice QCD, phenomenology, and experiment, highlighting connections between GPDs, the QCD energy–momentum tensor, and gravitational form factors that reveal mass, spin, and internal pressure profiles. Key progress includes neutron-target DVCS flavor separation, near-threshold gluon EMT form factors from J/ψ photoproduction, and the emergence of GTMDs as access points to quark orbital angular momentum, all supported by lattice QCD in both Breit and asymmetric frames. The report also outlines experimental roadmaps for JLab (including SoLID), COMPASS, J-PARC, and future facilities (EIC, EicC) to achieve quantitative, tomographic 3D imaging of nucleons and nuclei, integrating experimental data with lattice and phenomenological modeling. Together, these developments move hadron tomography toward precise, multi-channel determinations of GPDs, EMT form factors, and the spatial–momentum correlations that underpin QCD dynamics and mass-spin decomposition in hadrons.

Abstract

Generalized Parton Distributions (GPDs) have emerged as a powerful framework for exploring the internal structure of hadrons in terms of their partonic constituents. Over the past three decades, the field has witnessed significant theoretical and experimental advancements. The interpretation of GPDs in impact parameter space offers a vivid three-dimensional visualization of hadron structure, correlating longitudinal momentum and transverse spatial distributions, thereby enabling tomographic imaging of hadrons. Furthermore, the link between GPDs and the matrix elements of the QCD energy-momentum tensor provides access to fundamental properties of hadrons, including spin decomposition and internal pressure distributions. Notably, recent analyses of Deeply Virtual Compton Scattering (DVCS) data have enabled the empirical extraction of the quark pressure profile inside the proton. This white paper presents an overview of recent developments in GPD theory and phenomenology, as well as progress in lattice QCD studies. It outlines the prospects for advancing our understanding of hadron structure through the next generation of dedicated experiments, including the extension of the Jefferson Lab 12~GeV program (and its potential 22~GeV upgrade), J-PARC, COMPASS/AMBER, LHC ultra-peripheral collisions, and the future electron-ion colliders EIC and EicC.

Figures (68)

• Figure 1: Overview on the kinematic coverage of previous, current, and future DIS experiments. As an example, the available kinematic points from published data of the DVCS process are given for the different experiments. This figure is taken from Ref Diehl:2023nmm. We additionally included the kinematical range of the planned EicC experimental facility taken from Fig. 2 of Ref. Cao:2023wyz and JLab 22 GeV, Fig. 17 of Ref. Accardi:2023chb.
• Figure 2: Exclusive processes involving GPDs: deeply virtual Compton scattering (a); hard exclusive electroproduction of mesons (b), (c). $Q^2=-q^2$ is the virtuality of the virtual photon; $x$ is the average fractional longitudinal momentum of the active parton, and $\xi$ is the skewness variable that characterizes the longitudinal momentum transfer between the initial and the final nucleon states. The Mandelstam variable $t$ represents the invariant momentum transfer between the initial and final nucleons. The DAs refer to the distribution amplitudes of the produced mesons.
• Figure 3: ERBL and DGLAP regions of the GPDs and corresponding partonic interpretation in the three regions separated by the cross-over lines $x = \pm \xi$.
• Figure 4: Complimentary exclusive processes involving GPDs. (a): timelike Compton scattering (TCS). (b): double deeply virtual Compton scattering (DDVCS); $Q^2$=$-q^2$ is the virtuality of the space-like initial photon, and $Q'^2$=$q'^2$ is the virtuality of the final time-like photon. (c): Meson-beam induced production of a lepton pair.
• Figure 5: Top panel: the $x$-dependence of the proton’s transverse charge radius. Bottom panel: artistic illustration of the increasing quark density and transverse extent as a function of $x$. The figure is adapted from Ref. Dupre:2017hfs.