3D Femtography of the Nucleon Using Generalized Parton Distribution Functions

This thesis is focused on the phenomenological study of hadron three dimensional structure using generalized parton distributions (GPDs) as a tool to investigate spin / orbital angular momentum (OAM) as an emergent phenomenon of quantum chromodynamics (QCD). In particular, we have developed a parameterization of quark and gluon GPDs at leading twist to study the mechanical properties of the proton. Included in this parameterization, we have studied the generalized transverse momentum dependent parton distributions (GTMDs) / Wigner distributions. Complementary to my theoretical study, I have developed a novel extraction of experimental observables from data using phenomenological and artificial intelligence (AI) methods.

The field of 3D femtography of the nucleon using GPDs was initiated in 1996 with the discovery of the connection between the phase space distributions that describe angular momentum of the partons, GPDs, and exclusive scattering processes. Since then, significant efforts have been made both theoretically and experimentally to establish a connection between the measured cross section and the images of the quarks and gluons inside of the proton. This chain of links is extensive and over the past 25 years there have been numerous advances in understanding how to disentangle measured observables.

Deeply virtual Compton scattering (DVCS) is an exclusive experiment similar to elastic electron-proton scattering; therefore, we can expect a similar cross section organization in terms of electric and magnetic pieces. Crucial to the extraction of elastic form factors from experimental data was the separation of an electric and magnetic term in the cross section. Recently at UVA we have calculated and re-organized the cross section of DVCS keeping this fact in mind. In particular, we have been able to identify the electric and magnetic components of the interference contribution to the total cross section where CFFs enter linearly.

By exploiting linear relations in the interference cross section terms only visible with our re-organization of the cross section, we can separately extract the real and imaginary parts of the CFFs H and E from unpolarized and polarized DVCS data. This novel application of a Rosenbluth-like separation to the cross section for DVCS is detailed in subsequent chapters. We demonstrate that when using this extraction technique the scale dependence changes crucially when compared to other commonly used formalism. A careful organization of the DVCS cross section, and a novel way to extract CFFs, is crucial to making first strides towards the development of 3D images of the proton.

There exists a need to develop advanced theoretical parameterizations of GPDs and numerical perturbative QCD evolution tools to constrain experimental observables at leading order (LO) and beyond. We present the results of a parameterization of gluon, quark, and antiquark GPDs at LO using an overlap scalar diquark model in which we evolve the GPDs using a numerical code developed at UVa. The GPD parameterizations are constrained using a recursive fitting procedure, where, in the forward limit we determine the parameters of the model using deep inelastic scattering data. Once we fit the forward limit parameters we introduce the momentum transfer variable, t, which we constrain using Lattice QCD calculations of the quark and gluon gravitational form factors. To compare model calculations to experimental data, we use a numerical framework to evolve the GPDs at LO. We are working towards the inclusion and calculation of next to leading order (NLO) evolution kernels as well as NLO Wilson coefficient functions for Compton form factor calculations.

Using state of the art machine learning techniques in collaboration with the data science institute at UVA we have developed a robust, deep neural network (DNN) architecture to model the DVCS cross section. We have designed the architecture so that it includes state of the art neural network (NN) techniques written in Python TensorFlow such as dropout and stochastic gradient descent with momentum. Our current work is focused on developing a supervised deep neural network approach to the extraction of Compton form factors from DVCS data. Establishing a relationship between experimental error and CFF error is key to understanding the precision needed from future experimental efforts in order to disentangle observables from data. We have also proposed the use of a reinforcement learning (RL) hybrid semi-supervised algorithm to extract GPDs from CFFs, creating a unique opportunity to use AI techniques for femtography.