[Theory@QGT]

The majority of the visible matter in the universe is built from protons and neutrons, and the nuclei they compose. The proton and neutron are not elementary particles but are themselves composed of fundamental particles called quarks and gluons. Understanding how quarks and gluons build the visible universe is one of the grand challenges of modern science. Over the last several decades, tremendous progress has been made in mapping one-dimensional projections of the quarks and gluons inside protons and neutrons. However, to address this grand challenge, a three-dimensional mapping of the motion and spatial location of these quarks and gluons inside protons and neutrons is needed. This endeavor can help address essential questions that currently remain unanswered: How do the spin and orbital degrees of freedom of quarks and gluons within the nucleon combine to make up its total spin? What is the origin of the mass of the nucleon and other hadrons? Do gravitational form factors inform us about the origin of mass, and can they be extracted from measurements? Where are the quarks and gluons located within the nucleon? How does the quark-gluon structure of the nucleon change when it is bound in the nucleus? All these urgent questions are stimulating considerable theoretical and experimental investigations, and major facilities have been and will be built to explore them.

It is now well established that the three-dimensional generalized parton distributions (GPDs) of quarks and gluons hold the key to answering many of these questions. GPDs detail how the quarks and gluons respond to probes that change the nucleon’s momentum and hold the key to understanding many aspects of quark and gluon dynamics. Extracting GPDs from experimental measurements is one of the major research areas in various hadron physics facilities, including HERMES and COMPASS in Europe, and Jefferson Lab in the US. With ongoing experimental efforts at the 12 GeV upgrade of Jefferson Lab and endeavors at a forthcoming Electron-Ion Collider (EIC), it is critical to build the theoretical framework to interpret this experimental data. It is, therefore, timely to organize a theoretical topical collaboration focusing on proton, neutron, and nuclear GPDs.

To achieve this, we have established the Quark-Gluon Tomography (QGT) Collaboration to address the “3D quark-gluon structure of hadrons: mass, spin, and tomography.” This collaboration has three pillars – theory, lattice QCD, and phenomenology – which will develop a strong synergy between them and thereby deliver new insights into the grand challenge questions outlined above.

The theory advances will focus on the foundation of applying QCD factorization theorems, including higher-order perturbative corrections and all-order resummations, to DVCS and other relevant hard exclusive processes with the goal of extracting GPDs. The theory pillar will also provide the necessary ingredients to extract the GPDs from a global analysis. In addition, we will explore non-perturbative methods to provide important insight to describe the GPDs, which can lead to a physics motivated parameterization for the global analysis.

In particular, our research will focus on the following subjects:

(1) Theory Advances in Deeply Virtual Compton Scattering

(2) Gluon Tomography with Exclusive Heavy Quarkonium Production

(3) New Processes and Observables for Probing GPDs

(4) Non-perturbative Methods for GPDs and Hadron Tomography

(5) Beyond GPDs: Wigner Distributions

The milestones from the theory working group are in three main categories: 1) application of perturbative QCD to hard exclusive processes; 2) non-perturbative methods, including and the Covariant Parton Model; and 3) processes at small-x.

Year 1: Analyze factorization for exclusive quarkonia production at leading power for all regions using SCET and NRQCD, including the large and small $Q^2$ regions and quarkonia production at threshold

Apply the light-front Hamiltonian method to compute the GPDs, explore the nucleon spin/mass sum rule, and help to unveil the parton correlation due to strong interaction non-perturbative physics

Year 2: Make quantitative connection of the GPD factorization formalism to the CGC/color-dipole formalism for various exclusive processes

Apply the Covariant Parton Model to the GPDs of quark and gluons, eventually the parton Wigner distributions

Year 3: Use SCET to investigate factorization at subleading power in DVCS, including hadron mass corrections and the factorization and resummation of potential endpoint singularities

Year 4: Perform large-$N_c$ analysis of hard exclusive pion production with $N \rightarrow \Delta$ transitions and a combined chiral $\times 1/N_c$ analysis of nucleon energy-momentum tensor form factors

Quantitative study of hard diffractive dijet and di-hadron production at future EIC and explore novel processes to probe the quark/gluon Wigner distribution in the valence and moderate $x$ region

Year 5: Study relativistic corrections and other subleading effects in heavy quarkonia production for cases where such corrections are likely to be important