Generalized Parton Distributions

TL;DR

This paper surveys the theoretical framework of generalized parton distributions (GPDs) and generalized distribution amplitudes (GDAs), connecting inclusive and exclusive hadron structure to a unified, three-dimensional picture. It details definitions, kinematics, evolution, and the wave-function (overlap) representations that underpin GPDs/GDAs, and it elaborates on the polynomiality, positivity, and Mellin-moment structures that constrain these objects. The work reviews dynamics and modeling strategies (double distributions, D-terms, chiralsoliton and large-Nc approaches) and discusses a wide array of exclusive processes (DVCS, meson electroproduction, two-photon processes) within a leading-power factorization framework, including higher-twist corrections and their phenomenological implications. Finally, it surveys the small-x regime, nuclei, and transitions to excited baryons, highlighting how GPDs encode orbital angular momentum, transverse imaging, and hadronization dynamics with significant implications for understanding the nucleon’s spin and spatial structure. The compiled theory provides a comprehensive toolkit for extracting 3D parton structure from exclusive scattering and for connecting hadron structure across diverse high-energy processes.

Abstract

We give an overview of the theory for generalized parton distributions. Topics covered are their general properties and physical interpretation, the possibility to explore the three-dimensional structure of hadrons at parton level, their potential to unravel the spin structure of the nucleon, their role in small-x physics, and efforts to model their dynamics. We review our understanding of the reactions where generalized parton distributions occur, to leading power accuracy and beyond, and present strategies for phenomenological analysis. We emphasize the close connection between generalized parton distributions and generalized distribution amplitudes, whose properties and physics we also present. We finally discuss the use of these quantities for describing soft contributions to exclusive processes at large energy and momentum transfer.

Figures (44)

• Figure 1: (a) Handbag diagram for the forward Compton amplitude $\gamma^*p \to \gamma^*p$, whose imaginary part gives the DIS cross section. (b) Handbag diagram for DVCS in the region $\xi<x<1$. (c) The same in the region $-\xi<x<\xi$. Momentum fractions $x$ and $\xi$ refer to the average hadron momentum $\frac{1}{2}(p+p')$. A second diagram is obtained in each case by interchanging the photon vertices.
• Figure 2: Diagrams for hard meson production $\gamma^* p \to M p$ with (a) quark and (b) gluon GPDs.
• Figure 3: Handbag diagrams for the annihilation of $\gamma^*\gamma$ into a $p\bar{p}$-pair (a) and into a single pion (b). Momentum fractions $z$ and $\zeta$ refer to the sum of momenta in the final state.
• Figure 4: Hadron and parton plus-momenta in the parameterization of (a): Ji Ji:1998pc and (b): Radyushkin Radyushkin:1997ki.
• Figure 5: The parton interpretation of GPDs in the three $x$-intervals $[-1,-\xi]$, $[-\xi,\xi]$, and $[\xi,1]$.