Applying perturbative QCD to hard exclusive electroproduction processes one is required to introduce generalized parton distributions. In this talk, I discuss double and skewed distributions, their basic structure, relation to hadronic form factors and usual ("forward") parton densities, modeling SPDs and some recent applications.
1. GENERALIZED PARTON DISTRIBUTIONS
The long-distance dynamics information in the perturbative QCD description of deeply virtual Compton scattering and hard exclusive electroproduction is accumulated in nonforward matrix elements (p -r I O I P) of quark and gluon light-cone operators [1][2][3][4] . They can be parametrized by two basic types of nonperturbative functions. The double distributions (DDs) F(x, y; t) [2,5] specify the Sudakov light-cone "plus" fractions xp + and yr + of the initial hadron momentum p and the momentum transfer r carried by the initial parton. Treating the proportionality coefficient ff -r+/p + as an independent parameter one can introduce an alternative description in terms of the nonforward parton distributions (NFPDs) ~'ยข(X; t) with X = x + y~ being the total fraction of the initial hadron momentum taken by the initial parton. The shape of NFPDs explicitly depends on the parameter ~ characterizing the skewedness of the relevant nonforward matrix element. This parametrization of nonforward matrix elements by ~'ยข(X; t) is similar to that proposed by X. Ji [1] who introduced off-forward parton distributions (OFPDs) H(~, ~; t) in which the parton momenta and the skewedness parameter ~ -r+/2P + are measured in units of the average hadron momentum P = (p + if)~2. There are simple relations between the two versions of the skewedness parameter: ~ = ~/(2 -~). They both satisfy the restriction 0 < ~,~ < 1. OFPDs and NFPDs [2,3] can be treated as particular forms of skewed patton distributions (SPDs). One can also introduce the version of DDs ("a-DDs" [5]) in which the active parton momentum is written in terms of symmetric variables k + = xP + + (1 + a)r+/2.
2. COMPTON AMPLITUDES
Compton scattering in its various versions provides a unique tool for studying many aspects of hadronic structure. A general Compton amplitude is a four-point function