Position space interpretation for generalized parton distributions

Generalized parton distributions (GPDs) [1] have attracted significant interest since it has been recognized that they can not only be probed in deeply virtual Compton scattering experiments but can also be related to the orbital angular momentum carried by quarks in the nucleon [2]. However, remarkably little is still known about the physical interpretation of GPDs, and one may ask the question: suppose, about 10-15 years from now, after a combined effort from experiment, simulation and theory, we know how these functions (i.e. GPDs) look like for the nucleon. What is it, in simple physical terms, that we will have learned about the structure of the nucleon? Of course, we will have learned something about the orbital angular momentum carried by the quarks [2], but is that all there is? In these notes, I will discuss another interesting piece of information that can be extracted from GPDs, namely how partons are distributed in the transverse plane. In nonrelativistic quantum mechanics, the physics of form factors is illucidated by transforming to the center of mass frame and by interpreting the Fourier transform of form factors as charge distributions in that frame. GPDs [1] are the form factors of the same operators [light cone correlators Ôq(x, 0⊥)] whose forward matrix elements also yield the usual (forward) parton distribution functions (PDFs). For example, the unpolarized PDF q(x) can be expressed in the form q(x) = 〈p, λ|Ôq(x, 0⊥)|p, λ〉, (1)