Generalized Parton Distributions: 3D Quark/Gluon Imaging of the Nucleon

Generalized parton distributions (GPDs) unify the concepts of the nucleon elastic form factors (measured in elastic eN scattering) and parton distributions (measured in inclusive deep-inelastic eN scattering). GPDs describe the form factors for the emission and absorption of a quark/gluon by a fast-moving nucleon, depending on the quark's longitudinal momentum fraction, and the invariant momentum transfer to the nucleon, t. Their Fourier transform with respect to t describes the spatial distribution of quarks in the transverse plane and provides us with a 3D image of the quark and gluon structure of the nucleon in QCD ("nucleon tomography"). This new representation provides a natural framework for describing effects of quark polarization and orbital motion (transverse momentum) in hard scattering processes and offers unprecedented possibilities to visualize the nucleon as an extended object. It also plays an important role in describing high-energy NN collisions with hard processes, such as Higgs boson production at the LHC.

Deeply virtual Compton scattering (left), and deeply virtual meson production (right)

GPDs can be probed in exclusive eN scattering processes, such as deeply virtual Compton scattering (DVCS) and meson production. At large momentum transfer, Q² >> 1 GeV², the production process happens in the reaction of the virtual photon with a single quark ("factorization"). The study of these processes and the extraction of the GPDs are one of the prime objectives of the 12 GeV Upgrade of CEBAF. Measurements of DVCS at 6 GeV indicate the applicability of the GPD-based description. Researchers at the JLab Theory Center develop the methods for the analysis of these processes, construct phenomenological models for the GPDs, and relate the information contained in the GPDs to that obtained from other nucleon observables.

References: 
A. V. Belitsky and A. V. Radyushkin, Phys. Rept. 418 (2005) 1
M. Guidal, M. V. Polyakov, A. V. Radyushkin and M. Vanderhaeghen, Phys. Rev. D 72 (2005) 054013
L. Frankfurt, M. Strikman and C. Weiss, Ann. Rev. Nucl. Part. Sci. 55 (2005) 403