Generalized parton distributions and the structure of the nucleon

TL;DR

This review synthesizes the theoretical framework, modeling approaches, and experimental status of generalized parton distributions (GPDs) as a tool to map nucleon structure in momentum and position space. It clarifies how GPDs encode correlations between partons, interpolate between PDFs and form factors, and provide 3D imaging through impact-parameter space; it also explains how Ji's sum rules connect GPD moments to quark and gluon angular momentum. The survey covers formal properties (polynomiality, sum rules, positivity), various modeling schemes (double distributions, dual parametrization, χQSM, CQMs, meson-cloud models), and the status of DVCS and hard exclusive meson production as experimental probes, highlighting the roadmap to a comprehensive, lattice-constrained, experimentally constrained understanding of the nucleon. The work underscores the importance of global analyses and future facilities (e.g., EIC) to map quark and gluon GPDs across kinematic regimes. Overall, GPDs provide a principled framework to access the multidimensional spin and momentum structure of the nucleon with growing experimental and theoretical support.

Abstract

Generalized parton distributions have been introduced in recent years as a suitable theoretical tool to study the structure of the nucleon. Unifying the concepts of parton distributions and hadronic form factors, they provide a comprehensive framework for describing the quark and gluon structure of the nucleon. In this review their formal properties and modeling are discussed, summarizing the most recent developments in the phenomenological description of these functions. The status of available data is also presented.

Figures (23)

• Figure 1: (a) Kinematic variables in the symmetric frame of reference; (b) parametrization of the GPD $H^q(x,\xi,t)$ in terms of momentum fractions.
• Figure 2: Diagrams showing $\xi$ symmetry of GPDs: a) $x>\xi$, b) $-\xi< x<\xi$, c) $x<-\xi$.
• Figure 3: The isosinglet distribution $H(x,\xi,\Delta^2) = H^u(x,\xi,\Delta^2) + H^d(x,\xi,\Delta^2)$ in the forward limit, $\Delta^2=0$ and $\xi=0$, (left panel) and for $\Delta^2_\perp = -\Delta^2 -\xi^2M_N^2 = 0$ and $\xi = 0.3$ (right panel). Dashed lines for the contribution from the discrete level; dashed-dotted lines for the contribution from the Dirac continuum; solid lines for the total contribution PPPBGW98.
• Figure 4: Deeply virtual Compton scattering from the virtual (a) baryon and (b) meson components of a dressed nucleon.
• Figure 5: The spin averaged ($H^q$, three upper panels) and the helicity flip ($E^q$, three lower panels) generalized parton distributions for the $u$ (left panels) and $d$ (right panels) flavours, at fixed values of $\xi$ and $t$ as indicated. Dashed-dotted curves: bare contribution. Dashed curves: contribution from the active baryon. Dotted curves: contribution from the active meson. Solid curves: total result.