Hard Exclusive Reactions and the Structure of Hadrons

TL;DR

The paper develops generalized parton distributions (GPDs) as a unifying description of nucleon structure relevant to hard exclusive processes. It combines formal GPD properties (polynomiality, sum rules, chiral features) with large-N_c and chiral-quark-soliton model calculations to build physically motivated parametrizations, including the D-term and Wandzura-Wilczek relations for twist-3. It then systematically connects these GPDs to observable quantities in deeply virtual Compton scattering and hard meson electroproduction, highlighting how DVCS and various meson channels can probe quark angular momentum, flavor structure, and chiral dynamics. The work also discusses N→Δ and N→Y transitions, SU(3) relations, and the role of pion/kaon poles, outlining experimental strategies (DVCS observables, vector and pseudoscalar meson production, and spin asymmetries) to map the three-variable GPD landscape and extract fundamental nucleon structure information.

Abstract

We outline in detail the properties of generalized parton distributions (GPDs), which contain new information on the structure of the nucleon and which enter the description of hard exclusive reactions. We highlight the physics content of the GPDs and discuss the quark GPDs in the large $N_c$ limit and within the context of the chiral quark-soliton model. Guided by this physics, we then present a general parametrization for these GPDs. Subsequently we discuss how these GPDs enter in a wide variety of hard electroproduction processes and how they can be accessed from them. We consider in detail deeply virtual Compton scattering and the hard electroproduction of mesons. We identify a list of key observables which are sensitive to the various nucleon structure aspects contained in the GPDs and which can be addressed by present and future experiments.

Figures (37)

• Figure 1: "Handbag" diagrams for DVCS.
• Figure 2: Factorization for the leading order hard meson electroproduction amplitude.
• Figure 3: Two-pion exchange graphs giving the chiral contributions to the nucleon form factors of the energy momentum tensor. The dashed lines represent the pion, and the solid lines represent the nucleon. The black blob is the operator of the energy momentum tensor.
• Figure 4: The GPD $H^u (x, \xi, t)+H^d (x, \xi, t)$ as a function of $x$ at $\xi = 0.3$ and $t=t_{\rm min}=-0.35$ GeV$^2$. Dashed curve: contribution from valence level. Dashed-dotted curve:contribution of the Dirac continuum. Solid curve: the total distribution (sum of the dashed and dashed-dotted curves). The vertical lines mark the crossover points $x=\pm\xi$.
• Figure 5: Ratio Eq. (\ref{['R-ratio']}) as a function of $x$ showing the deviation from the factorization ansatz for the $t$-dependence of the GPD $H$ for the values of $\xi=0$ (filled circles) and $\xi=0.2$ (open circles) with $t_0=-4 m_N^2\xi^2/(1-\xi^2)$ and $t_1=t_0-0.5$ GeV$^2$.