On the Distribution of Partons in the Transverse Plane

Parton densities are among the most important sources of information on hadron structure at the level of quarks and gluons. The conventional densities describe the distribution of longitudinal momentum and helicity carried by partons in a fast-moving hadron. Generalized parton distributions (GPDs) complement this essentially one-dimensional picture with information on the directions transverse to the one in which the hadron moves.1,2 In this talk I present main results of a study of the interplay between transverse and longitudinal degrees of freedom.3 Thanks to short-distance factorization GPDs appear in exclusive scattering processes such as deeply virtual Compton scattering (γp → γp) and hard meson production. In such processes a finite momentum is transferred to the proton. As a consequence, GPDs depend on two longitudinal parton momentum fractions and in addition on the invariant momentum transfer t to the proton. Understanding the interplay between the two longitudinal parton momenta remains an outstanding task, and in the following I consider the simpler case where they are equal. The socalled skewness parameter ξ is then zero, and the distributions depend on a single longitudinal momentum fraction x and on t. At small x and not too large t, phenomenological experience from high-energy scattering suggests a simple parameterization4 H(x, t) ∼ x ′t) = x exp[ tα′ log(1/x) ] (1)