Symmetries and structure of skewed and double distributions

Extending the concept of parton densities onto nonforward matrix elements 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 and nonforward) parton distributions (SPDs) H(x,ξ;t), Fζ(X,t). The authors treat DDs as primary objects producing SPDs after integration. They emphasize the role of DDs in understanding interplay between (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 ζ or ξ. They propose simple ansaetze for DDs having correct spectral and symmetry properties and derive model expressions for SPDs satisfying all known constraints. Finally, they 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 [Xminusζ,X] (or [ x minus ξ, x + ξ])