Complex conformal spin partial wave expansion of generalized parton distributions and distribution amplitudes

We introduce a new representation of generalized parton distributions and generalized distribution amplitudes that is based on the partial wave decomposition with respect to the complex collinear conformal spin. This decomposition leads us to a versatile parameterization of these non-perturbative functions in terms of conformal moments, which are measurable for integer value on the lattice. This new representation has several advantages: basic properties and crossing relations are automatically implemented, a rather flexible parameterization is possible, the numerical treatment of evolution is simple and analytic approximation of scattering amplitudes can be given. We demonstrate this for simple examples. In particular, phenomenological considerations indicate that the t-dependence of Mellin moments is governed by Regge trajectories. The new representation is vital to Push the analysis of deeply virtual Compton scattering to next-to-next-to-leading order. (c) 2006 Elsevier B.V. All rights reserved.