We introduce a new representation of generalized parton distributions andgeneralized distribution amplitudes that is based on the partial wavedecomposition with respect to the complex collinear conformal spin. Thisdecomposition leads us to a versatile parameterization of thesenon-perturbative functions in terms of conformal moments, which are measurablefor integer value on the lattice. This new representation has severaladvantages: basic properties and crossing relations are automaticallyimplemented, a rather flexible parameterization is possible, the numericaltreatment of evolution is simple and analytic approximation of scatteringamplitudes can be given. We demonstrate this for simple examples. Inparticular, phenomenological considerations indicate that the t-dependence ofMellin moments is governed by Regge trajectories. The new representation isvital to push the analysis of deeply virtual Compton scattering tonext-to-next-to-leading order.
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