Parton distributions and lattice QCD calculations: toward 3D structure

TL;DR

This paper reviews recent progress in understanding the three-dimensional structure of hadrons through Parton Distribution Functions, Generalized Parton Distributions, and Transverse Momentum Dependent PDFs, combining experimental data and lattice QCD calculations.

Contribution

It provides an updated overview of advances in collinear and generalized PDFs, emphasizing the integration of lattice QCD and experimental efforts for hadron structure.

Findings

Progress in lattice QCD calculations of PDFs

Enhanced understanding of GPDs and TMD PDFs

Potential for future experimental and theoretical developments

Abstract

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.