Coordinate Space Representation and Average Radius 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.  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 at 10 GeV.  We compare the valence quarks to the gluon distribution through, i.a., average radii, a notion of distance inside the nucleon, and we present a novel result for the radius of the gluon density.  We also studied the effect of evolution, the normalization of the Fourier transforms through parton distribution functions in the off-forward limit of the GPDs, and the difference between matter and charge density in both the proton and the neutron.