ar X iv : h ep - p h / 02 01 11 9 v 1 1 4 Ja n 20 02 hep - ph / 0201119 SPIN AND OTHER ASPECTS OF GENERALIZED PARTON DISTRIBUTIONS 1

I discuss how generalized parton distribution probe various aspects of QCD bound states. Topics include the interplay between transverse and longitudinal structure, quantum mechanical interference, orbital angular momentum, helicity flip, and higher-spin targets. 1 Before talking about spin My assignment is to speak about spin aspects of generalized parton distributions. Before doing so I would however like to point out some of the information they contain even if the spin degrees of freedom are all averaged over. The usual parton densities we are accustomed with are expectation values of quark or gluon operators for a hadron state, and generalized parton distributions [1, 2, 3, 4] are their natural extension to non-forward kinematics. This is readily seen from the diagrams for Compton scattering in the deeply virtual limit (Fig. 1). Since an off-shell photon turns into an on-shell one, the two proton states in the hadronic matrix element must have different momenta. A useful set of variables describing the kinematics are x and ξ, parameterizing longitudinal momentum fractions in a frame where both protons move fast, and the Mandelstam invariant t = (p ′ − p) 2 , which one can trade for the transverse momentum transfer (p ′ − p) ⊥. This tells us immediately that we are in a position to probe the transverse and the longitudinal structure of a fast moving proton in a correlated manner. Setting ξ and t to zero one recovers the usual parton distributions, which have the intuitive interpretation of a density in longitudinal parton momentum. Burkardt [5] has shown that for ξ = 0 we retain a density interpretation if we perform a Fourier transformation from (p ′ − p) ⊥ to impact parameter, which measures the transverse distance of the struck quark from the proton's center. Generalized parton distributions at ξ = 0 thus describe the transverse distribution of partons with a given longitudinal momentum fraction x.