  In the framework of quantum chromodynamics (QCD), parton distribution
functions (PDFs) quantify how the momentum and spin of a hadron are divided
among its quark and gluon constituents. Two main approaches exist to determine
PDFs. The first approach, based on QCD factorization theorems, realizes a QCD
analysis of a suitable set of hard-scattering measurements, often using a
variety of hadronic observables. The second approach, based on first-principle
operator definitions of PDFs, uses lattice QCD to compute directly some
PDF-related quantities, such as their moments. Motivated by recent progress in
both approaches, in this document we present an overview of lattice-QCD and
global-analysis techniques used to determine unpolarized and polarized proton
PDFs and their moments. We provide benchmark numbers to validate present and
future lattice-QCD calculations and we illustrate how they could be used to
reduce the PDF uncertainties in current unpolarized and polarized global
analyses. This document represents a first step towards establishing a common
language between the two communities, to foster dialogue and to further improve
our knowledge of PDFs.
