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 left-angle p'|nO(0,z)|np right-angle of quark and gluon light-cone operators. In our previous papers we used two types of nonperturbative functions parametrizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions Fζ(X;t). Here we discuss in more detail the double distributions (DD close-quote s) and evolution equations which they satisfy. We propose simple models for F(x,y;t=0) DD close-quote 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, we obtain self-consistent models for the ζ dependence of nonforward distributions. We 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). copyright 1998 The American Physical Society