Double distributions and evolution equations

Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements < p prime |O(0,z)|p > of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions Fζ(X;t). Here they discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the ζ-dependence of nonforward distributions. They show that, for small ζ, one can easily obtain nonforward distributions (in the X > ζ region) from the parton densities: Fζ (X;t=0) ∼ f(X-ζ/2)