The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD

Erratum to: Topical issue on Lattice Field Theory during the Covid-19 pandemic

[This corrects the article DOI: 10.1140/epja/s10050-021-00614-5.].

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

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.