Mapping Parton Distributions of Hadrons with Lattice QCD

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 three-dimensional structure of hadrons, which can be described by generalized parton distributions (GPDs), for example. In recent years, a breakthrough was made in calculating the Bjorken-$x$ dependence of PDFs in lattice QCD by using large-momentum effective theory (LaMET) and other similar frameworks. The breakthrough has led to the emergence and rapid development of direct calculations of Bjorken-$x$--dependent structure. In this review article, we show some of the recent progress made in lattice QCD in PDFs and GPDs and discuss future challenges.