Hadron structure from lattice quantum chromodynamics

Abstract

This is a review of hadron structure physics from lattice QCD. Throughout this report, we place emphasis on the contribution of lattice results to our understanding of a number of fundamental physics questions related to, e.g., the origin and distribution of the charge, magnetization, momentum and spin of hadrons. Following an introduction to some of the most important hadron structure observables, we summarize the methods and techniques employed for their calculation in lattice QCD. We briefly discuss the status of relevant chiral perturbation theory calculations needed for controlled extrapolations of the lattice results to the physical point. In the main part of this report, we give an overview of lattice calculations on hadron form factors, moments of (generalized) parton distributions, moments of hadron distribution amplitudes, and other important hadron structure observables. Whenever applicable, we compare with results from experiment and phenomenology, taking into account systematic uncertainties in the lattice computations. Finally, we discuss promising results based on new approaches, ideas and techniques, and close with remarks on future perspectives of the field.

Baryons as relativistic three-quark bound states

“…Nucleon form factor calculations in lattice QCD have made substantial progress in recent years. Whereas the early quenched calculations are summarized in the review articles [442,450], nowadays essentially all calculations are performed using dynamical fermions. Studies of electromagnetic nucleon form factors are available from various collaborations for N f = 2 [451][452][453][454][455], N f = 2 + 1 [397,[456][457][458][459][460][461][462] and N f = 2 + 1 + 1 flavours [463,464], including calculations nearly at the physical pion mass [397] which agree reasonably well with the experimental data.…”

Bessel-weighted asymmetries in semi-inclusive deep inelastic scattering

“…Taking x-moments is a standard ingredient in lattice computations of nucleon structure, see e.g., ref. [53] for a review. First exploratory studies of TMD PDFs on the lattice [38,39] focus to a large degree on computations of the lowest x-moment of distributions, but access to finite values of B L is also possible.…”

Quasi-Parton Distribution Functions: A Study in the Diquark Spectator Model

“…In recent years, however, evaluation of PDFs has been attempted in lattice QCD [7][8][9][10]. Since PDFs are defined as the non-local light-cone correlations which involve the real Minkowski time, the traditional lattice QCD approach does not allow one to compute the PDFs directly [11]; one can only calculate the lower moments of the PDFs, which are matrix elements of local operators [7,8].…”