Nuclear Medium Modifications of Hadrons from Generalized Parton Distributions

We study the structure of generalized parton distributions in spin 0 nuclei within a microscopic approach for nuclear dynamics. GPDs can be used on one side as tools to unravel the deep inelastic transverse structure of nuclei in terms of both transverse spatial and transverse momentum degrees of freedom. On the other, one can obtain information on GPDs themselves by observing how they become modified in the nuclear environment. We derive the structure of the nuclear deeply virtual Compton scattering tensor and generalized parton distributions at leading order in $Q$ in a field-theoretical framework. The nuclear generalized parton distributions are calculated using a two step process -- the convolution approach -- where the scattering process happens from a quark inside a nucleon, itself inside a nucleus, disregarding final state interactions with both the nuclear and nucleon debris. We point out that details of the nuclear long range interactions such as two-body currents, can be disregarded compared to the deep inelastic induced modifications of the bound GPDs. We show how the pattern of nuclear modifications predicted, and in particular the deviations of off-shell effects from the longitudinal convolution provide clear signals to be sought in experimental measurements. Finally, we find interesting relationships by studying Mellin moments in nuclei: in particular we predict the $A$-dependence for the $D$-term of GPDs within a microscopic approach, and the behavior with $t$ of the total momentum carried by quarks in a nucleus. The latter provides an important element for the evaluation of nuclear hadronization phenomena which are vital for interpreting current and future data at RHIC, HERMES and Jefferson Lab.