Gpds, Form Factors and Compton Scattering

As is well-known factorization is an important property of QCD whithout which we would not be able to calculate form factors or cross sections. Factorization into a hard parton-level subprocess to be calculated from perturbative QED and/or QCD, and soft hadronic matrix elements which are subject to non-perturbative QCD and are not calculable at present, has been shown to hold for a number of reactions provided a large scale, i.e. a large momentum transfer, is available. For other reactions factorization is a reasonable hypothesis. In the absence of a large scale we don’t know how to apply QCD and, for the interpretation of scattering reactions, we have to rely upon effective theories or phenomenological models as for instance the Regge pole one. For hard exclusive processes there are two different factorization schemes available. One of the schemes is the handbag factorization (see Fig. 1) where only one parton participates in the hard subprocess (e.g. γq → γq in Compton scattering) and the soft physics is encoded in generalized parton distributions (GPDs) . The handbag approach applies to deep virtual exclusive scattering (e.g. DVCS) where one of the photons has a large virtuality, Q, while the squared invariant momentum transfer, −t, from the ingoing hadron to the outgoing one is small. It also applies to wide-angle scattering (WACS) where Q is small while −t (and −u) are large . This class of reactions is the subject of my talk. For wide-angle scattering there is an alternative scheme, the leading-twist factorization . Here all valence quarks the involved hadrons are made off participate in the hard scattering