Generalized Parton Distributions

TL;DR

This work presents a unified framework (GPDs) for describing nonforward hadronic structure, linking inclusive PDFs, exclusive DAs, and form factors through double distributions and skewed parton distributions. It details their mathematical properties (polynomiality, support), evolution, and practical modeling approaches (DD- and SPD-based), and applies the formalism to DVCS and real Compton scattering, including twist-2 and kinematic twist-3 considerations. The paper also discusses the Polyakov-Weiss D-term, inequalities, and how SPDs encode information about angular momentum via Ji’s sum rule, offering a path to access orbital motion and spin structure in the proton. Overall, the work lays out a comprehensive theoretical architecture for extracting rich, multidimensional information about hadron structure from hard exclusive processes.

Abstract

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of the usual parton distributions for the case when long-distance information is accumulated in nondiagonal matrix elements of quark and gluon light-cone operators. I describe two types of nonperturbative functions parametrizing such matrix elements: double distributions and skewed parton distributions. I discuss their general properties, relation to the usual parton densities and form factors, evolution equations for both types of generalized parton distributions (GPD), models for GPDs and their applications in virtual and real Compton scattering.

Figures (13)

• Figure 1: Parton distribution function.
• Figure 2: $a)$ General Compton amplitude; $b)$$s$-channel handbag diagram; $c)$$u$-channel handbag diagram.
• Figure 3: Handbag diagrams and parton picture. $a)$ Virtual forward Compton amplitude expressed through the usual parton densities $f(x)$. $b)$ Form factor $\gamma^* \gamma \pi^0$ written in terms of the distribution amplitude $\varphi (\alpha)$.
• Figure 4: $a)$ Parton description of deeply virtual Compton scattering in terms of double distributions $f(x,\alpha;t)$. $b)$ Support region for $f(x,\alpha;t)$.
• Figure 5: Description of the nonforward matrix element in terms of $a)$ double distribution $f(x,\alpha;t)$ and $b)$ off-forward parton distribution $H(\tilde{x},\xi;t)$. $c)$ Integration lines for integrals relating OFPDs and DDs.