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Anatoly Radyushkin

Andreas Schaefer

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Institute for Nuclear Theory Workshop 03-2

Generalized Parton Distributions and Hard Exclusive Processes
High-Energy Scattering and Internal Structure of Hadrons

June 23, 2003 - August 29, 2003

Understanding the hadron structure, in particular, the proton and neutron, from the fundamental theory of strong interactions is one of the most important frontiers in nuclear and particle physics. In theory, lattice QCD, large Nc expansion, and effective field theories such as chiral perturbation theory have been explored as efficient tools to understand the many aspects of strong interactions. Experimentally, experiments at MIT-Bates, JLab, SLAC, FNAL, DESY, CERN, Mainz, and other facilities are making new and more precise measurements of the nucleon electromagnetic and weak form factors, polarized and unpolarized quark and gluon distributions, generalized parton distributions and many other important observables. The goal of this program is to bring together theorists and experimentalist working in the general area of hadronic physics to discuss and explore the intersections of new experimental data and innovative theoretical ideas. Topics surrounding high-energy scattering, spin physics, and generalized parton distributions are emaphasized, but other interesting subjects such as lattice computation of hadronic matrix elements, and chiral perturbation calculations, will be included as well.

High-energy processes are the main driving force towards unraveling the microscopic structure of hadrons. For decades, the cleanest experiments were lepton-hadron scattering at high momentum transfer which, on the one hand, have provided rich information on diverse properties of hadron constituents and, on the other, opened unexplored domains of polarized phenomena, high parton densities, etc. However, solely inclusive deeply inelastic scattering experiments are unable to provide an exhaustive multi-dimensional picture of hadrons. The high-energy exclusive processes are capable of probing physics from the short-distance parton level down to the scale of chiral symmetry breaking with the varied resolutions and, thus, offer the possibility of exploring the hadron structure from a different perspective.

The generalized parton distributions (GPD's) extend the well-known Feynman parton distribution and electromagnetic form factors of the nucleon to new kinematic dimensions. In the forward limit, these distributions reduce to the Feynman parton distributions. On the other hand, the first moment of GPD's give the electromagnetic form factors. In general, the GPD's contain much richer structural information of the nucleon than conventional observables. For instance, the second moment of some GPD's are related to the fractions of the nucleon spin carried separately in quarks and gluons, and certain other special kinematic limits of the GPD's are the orbital angular momentum distributions. >From the viewpoint of the form factors, the GPD's contain generalized form factors of a whole class of quark and gluon tensor operators. The one with the lowest spin corresponds to the electroweak currents. GPD's can also be defined for the transition between the nucleon state to the excited states such as the Delta resonance and N*, or more generally N-pi, NK, etc., final states.

The GPD's can be probed in a new class of hard exclusive processes. The simplest example is deeply-virtual Compton scattering (DVCS) in which leptons scatter in a deeply inelastic process from a nucleon target producing a high-energy real photon plus the recoiled nucleons. One can prove a factorization theorem for the process, according to which the cross section can be expressed as a convolution of the perturbatively calculable coefficient functions and GPD's. Other examples of hard exclusive processes are similar to DVCS with replacement of the real photon by mesons. The meson production processes provide powerful tools to access different spin and flavor combinations of the GPS's depending on the quantum number of mesons. DVCS and meson production in the deep-inelastic region has been observed at HERA. A number of experiments, including those at Jefferson Lab, HERMES at DESY, and COMPASS at CERN are vigorously pursuing the generalized parton distributions. The hard exclusive processes are one of the main physics motivations for the proposed facilities such as ELFE (European Lab For Electrons) in Europe and EIC (Electron-Ion Colliders) in the United States. A tremendous amount of theoretical work have been done in this new field in the last five years. DVCS and hard exclusive meson production have been shown to be factorizable to all orders in QCD perturbation theory. The coefficient functions have been computed to one-loop order and the anomalous dimensions of the twist-two operators, including mixing with the total derivative operators, have been computed to two-loop order. Hence, the next-to-leading order perturbative QCD formalism is completely established. Model calculations and parametrizations of the generalized parton distributions have been done at various levels of sophistication. Experimental cross sections including polarization asymmetries have been estimated for various existing and future facilities. There remain many theoretical and experimental challenges in the field that awaits further exploration. For instance, kinematic power corrections depending only on the leading twist distributions may be studied in the Wandzura-Wilczek approximation. Dynamical higher-twist corrections require simultaneous study of the higher-order coefficient functions and the matrix elements of higher-twist operators. Polarization effects in hard photon and meson production require more detailed theoretical investigation. Meson pair production in photon-photon collisions depends on the generalized parton distributions in the time-like region. Momentum dependence of the generalized form factors needs to be understood. The wide-angle real Compton scattering formalism needs an extension to include higher-twist contributions. The next-to-leading order formalism for all hard exclusive processes must be completed. Finally, a practical design for an ideal machine measuring hard exclusive processes is yet to be completed.

9/20/02 - webmaster