Speaker
Description
Generalized Parton Distributions (GPDs) and the exclusive processes that probe them present an important insight into hadronic structure. However, extracting GPDs from experimental data constitutes a challenging inverse problem. In this work we revisit the Finite Elements Method (FEM) to study GPDs via their double distribution (DD) representation, focusing on the Radon transform that connects DDs to GPDs. We investigate the existence and structure of "shadow" double distributions, DD functions whose associated physical observables all vanish identically, yet when added to physical DDs, can modify the GPD in the entire kinematic domain. Using the FEM discretization of the DD support, we quantify how experimental constraints, particularly measurements at different x and ξ values, progressively reduce the shadow DD solution space. This analysis reveals the fundamental relationship between experimental precision and the theoretical resolution with which we can reconstruct GPDs, providing a framework for optimizing future experimental programs targeting hadronic structure.