This paper is a review of recent progress in computing the internal structure of hadrons using lattice Quantum Chromodynamics (QCD). Lattice QCD (LQCD) is a way to put the equations of the strong force on a space–time grid so they can be solved numerically. The review highlights results for basic charges, form factors, and the low Mellin moments of parton distributions, and it summarizes newer methods that aim to extract the full dependence on the momentum fraction x of quarks and gluons inside hadrons.

The authors describe two complementary approaches. One set of results comes from traditional Mellin moments, which are averages of powers of the momentum fraction x and are computed from local operators on the lattice. The other approach extracts x-dependent distributions more directly using methods such as Large-Momentum Effective Theory (LaMET). These direct extractions typically use boosted hadrons with momenta Pz around 1.5–2 GeV, nonperturbative renormalization, and perturbative matching up to next-to-next-to-leading order (NNLO) to connect lattice numbers to the quantities used in experiments.

The review gives concrete examples and comparisons. Several groups have produced pion vector form factors and charge radii that agree with experimental values, though lattice errors are still larger. Different collaborations use different lattice setups: for example, one group reached Q2 (momentum-transfer squared) values up to about 2.5 GeV2 by working in a Breit frame, while others emphasize low-Q2 behavior or a range of pion masses. For the pion and kaon, recent lattice studies also report quark and gluon momentum fractions after doing continuum extrapolations and presenting results in a common MS renormalization convention at 2 GeV.

This work matters because the Electron–Ion Collider (EIC) aims to produce three-dimensional images of hadrons in terms of their quark and gluon content. Lattice QCD can supply inputs that help design detectors and interpret future measurements at the EIC and related experiments. For example, LQCD can provide percent-level precision for some charges and form factors, and it can offer independent determinations of moments and x-dependent distributions that feed into global analyses of experimental data.