Symmetries and structure of skewed and double distributions

Extending the concept of parton densities onto nonforward matrix elements 〈p′ | O(0,z) | p〉, one can use double distributions (DDs) f(x,α;t),F(x,y;t) or skewed (off&nonforward) parton distributions (SPDs) H(x̃,ξ;t),Fζ(X,t). The use of DDs is crucial for understanding interplay between X(x̃) and ζ(ξ) dependences of SPDs and securing the property that Nth moments of SPDs are Nth degree polynomials in the skewedness parameters ζ or ξ. Proposing simple ansätze for DDs, we derive model expressions for SPDs satisfying all known constraints. 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 [x̃−ξ,x̃+ξ]).