Global Deep Neural Network Modeling of Compton Form Factors Constrained from Local $\chi^2$ Maps Fits

Abstract

Over the past two decades, intense experimental efforts have focused on measuring observables that contribute to a three-dimensional description of the nucleon. Generalized Parton Distributions provide complementary insights into the internal structure and dynamics of hadrons, including information about the orbital angular momentum carried by quarks. The most direct process to access these distributions is Deeply Virtual Compton Scattering, in which the cross section can be expressed in terms of Compton Form Factors. These quantities are defined as convolutions of the Generalized Parton Distributions with coefficient functions derived in perturbative Quantum Chromodynamics. We extract the Compton Form Factors from Deeply Virtual Compton Scattering data collected at Jefferson Lab, including the most recent measurements in Hall A, using a novel local fitting technique based on $\chi^2$ mapping to constrain the real parts of the Compton Form Factors $\mathcal{H}, \mathcal{E}$ and $\widetilde{\mathcal{H}}$. They are determined independently in each kinematic bin for the unpolarized beam-target configuration under the twist-2 approximation, following the formalism developed by Belitsky, M\"uller, and Kirchner. The extracted Compton Form Factors are then used to train and regularize a deep neural network, enabling a global determination of their behavior with minimal model dependence. This procedure is validated and systematically studied using pseudodata generated with kinematics matching those of the experimental measurements.