Symmetries and structure of skewed and double distributions
A. V. Radyushkin
TL;DR
This paper develops the double-distribution (DD) formalism as the foundational description for nonforward parton matrix elements, from which skewed parton distributions (SPDs) and off-forward parton distributions (OFPDs) are derived by integration. DDs ensure crucial properties such as polynomiality of SPD moments and controlled nonanalyticities at skewness-related borders, while enabling flexible, physically motivated models. The authors propose simple, symmetry-respecting DD ansaetze and demonstrate how SPDs reduce to averaged forward densities in the small-skewedness limit, providing a practical bridge between forward PDFs and hard-exclusive processes like DVCS. Overall, the DD framework offers a consistent and constraining approach to modeling SPDs for DVCS and hard exclusive electroproduction.
Abstract
Extending the concept of parton densities onto nonforward matrix elements <p'|O(0,z)|p> of quark and gluon light-cone operators, one can use two types of nonperturbative functions: double distributions (DDs) f(x,α;t), F(x,y;t) and skewed (off&nonforward) parton distributions (SPDs) H(x,ξ;t), F_ζ(X,t). We treat DDs as primary objects producing SPDs after integration. We emphasize the role of DDs in understanding interplay between X (x) and ζ(ξ) dependences of SPDs.In particular, the use of DDs is crucial to secure the polynomiality condition: Nth moments of SPDs are Nth degree polynomials in the relevant skewedness parameter ζor ξ. We propose simple ansaetze for DDs having correct spectral and symmetry properties and derive model expressions for SPDs satisfying all known constraints. Finally, we argue that for small skewedness, one can obtain SPDs from the usual parton densities by averaging the latter with an appropriate weight over the region [X-ζ,X] (or [x - ξ, x + ξ]).