Overview of lattice calculations of the $x$-dependence of PDFs, GPDs and TMDs

Abstract

For a long time, lattice QCD was unable to address the $x$-dependence of partonic distributions, direct access to which is impossible in Euclidean spacetime. Recent years have brought a breakthrough for such calculations when it was realized that partonic light-cone correlations can be accessed through spatial correlations computable on the lattice. Appropriately devised observables can be factorized into physical PDFs via a perturbative procedure called matching, analogous to the standard factorization of experimental cross sections. In this short review, aimed at a broader high-energy and nuclear physics community, we discuss the recent highlights of this research program. Key concepts are outlined, followed by a case study illustrating the typical stage of current lattice extractions and by a brief review of the most recent explorations. We finalize with a number of messages for the prospects of lattice determinations of partonic structure.

Comments: 12 pages, 2 figures; invited plenary talk at the Virtual Tribute to Quark Confinement and the Hadron Spectrum 2021, August 2-6, 2021