One of the most fascinating possibilities of modern electron-scattering experiments is that they can measure the spatial distribution of quarks and gluons, providing actual three-dimensional images of the proton at the femtometer scale. The reconstruction of spatial images from scattering experiments by way of Fourier transform of the observed scattering pattern is a technique widely used in physics, e.g., in X-ray scattering from crystals. Recently, it was discovered how to extend this technique to the spatial distribution of quarks and gluons within the proton, using processes that probe the proton at a tiny resolution scale. The spatial distribution of the partons is encoded in the generalized parton distributions, a rich formalism that both unifies existing descriptions of proton structure and takes a giant step into unknown territory. Mapping out the GPDs is an ambitious program that requires the energies and high luminosities of the 12 GeV CEBAF Upgrade and, for the gluons, a future Electron-Ion Collider. Are the up quarks, the down quarks, and the gluons in the proton equally distributed in space? Are the quarks more polarized in the center than at the periphery? Answers to questions like these await and will revolutionize our knowledge of proton structure. Finally, encoded in the GPDs is yet another secret: the orbital angular momentum of the quarks and gluons. With the GPDs, we not only obtain still photographs of the quarks, but we catch them in action as well.

The figure shows illustrations of the spatial distribution of up quarks that will become accessible with the 12 GeV CEBAF Upgrade. The red and green forms outline the regions of highest quark density in a proton viewed by a beam traveling along the z axis. The images are for two different values of quark momentum fraction x, showing the expected difference in the spatial distribution of high and low x.

Source: Frontiers of Nuclear Science, A Long Range Plan, Nuclear Science Advisory Committee, December 2007