Nonforward Parton Distributions

TL;DR

This work develops a comprehensive framework for nonforward parton distributions, introducing two equivalent descriptions—the universal double distributions F(x,y;t) and the skewed, X dependent F_ζ(X;t)—and shows how they underpin hard exclusive processes like DVCS and meson electroproduction. Using scalar toy models and a rigorous α-representation, the paper derives spectral properties, factorization conditions, and all-order perturbative expansions, then extends the formalism to full QCD with quarks and gluons and their evolution kernels. It identifies the regions where DGLAP and BL type evolution apply, analyzes asymptotic solutions, and discusses end-point and Sudakov considerations crucial for factorization. The results provide a formal foundation for connecting inclusive parton distributions to exclusive amplitudes, enabling quantitative treatment of DVCS and gluonic contributions in hard exclusive processes.

Abstract

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements <p'|O|p> of quark and gluon light-cone operators. We describe two types of nonperturbative functions parametrizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F_ζ(X;t), discuss their spectral properties, evolution equations which they satisfy, basic uses and general aspects of factorization for hard exclusive processes.

Figures (11)

• Figure 1: Scalar model analogs of $a),b)$ virtual forward Compton amplitude and $c),d)$ deeply virtual Compton scattering.
• Figure 2: Longitudinal momentum flow for two components of the asymmetric distribution function ${\cal F}_{\zeta}(X)$: a)$X > \zeta$ and b)$X < \zeta$.
• Figure 3: $a)$ Structure of momentum integral defining the asymmetric distribution function ${\cal F}_{\zeta}(X)$. $b)$ Cut of parton-hadron amplitude corresponding to the residue for the region $X > \zeta$. $c)$ Cut of parton-hadron amplitude corresponding to the residue for the region $X < \zeta$.
• Figure 4: Handbag diagram for deeply virtual Compton scattering.
• Figure 5: Four-point amplitude corresponding to the deeply virtual Compton scattering.