Coordinate Space Representation of Quark and Gluon Generalized Parton Distribution Functions

Two-dimensional Fourier transforms of generalized parton distributions (GPDs) provide insight into matter, charge, and radial distributions of the quarks and gluons inside the nucleon.   We present an explicit calculation of such transforms in a spectator model framework using parametric analytic forms of GPDs, originally constrained using deeply virtual Compton scattering and lattice QCD data.  Our calculations were performed for several values of the momentum fraction X and evolved using perturbative QCD from the initial scale Q₀ to the scale of the data.  We studied the effect of evolution, the difference between matter and charge density in both the proton and the neutron, and the location of the gluon distribution relative to the valence quarks.