Extraction of Generalized Parton Distribution Observables from Deeply Virtual Electron Proton Scattering Experiments

We provide the general expression of the cross section for exclusive deeply virtual photon electroproduction from a spin-$1/2$ target using current parametrizations of the off-forward correlation function in a nucleon for different beam and target polarization configurations up to twist-three accuracy. All contributions to the cross section including deeply virtual Compton scattering, the Bethe-Heitler process, and their interference, are described within a helicity-amplitude-based framework which is also relativistically covariant and readily applicable to both the laboratory frame and in a collider kinematic setting. Our formalism renders a clear physical interpretation of the various components of the cross section by making a connection with the known characteristic structure of the electron scattering coincidence reactions. In particular, we focus on the total angular momentum, ${J}_{z}$, and on the orbital angular momentum, ${L}_{z}$. On one side, we uncover an avenue to a precise extraction of ${J}_{z}$, given by the combination of generalized parton distributions, $H+E$, through a generalization of the Rosenbluth separation method used in elastic electron proton scattering. On the other side, we single out for the first time, the twist-three angular modulations of the cross section that are sensitive to ${L}_{z}$. The proposed generalized Rosenbluth technique adds constraints and can be extended to additional observables relevant to the mapping of the three-dimensional structure of the nucleon.