Parton distribution and correlation functions describe the relation
between a hadron and the quarks and gluons (or partons) within it, and
carry rich information on hadron’s partonic structure. They cannot be
calculated by QCD perturbation theory, and have been extracted from
experimental data of high energy scattering cross sections with the
aid of QCD factorization. Parton distribution functions are the
simplest of all correlation functions. Without them, we would not be
able to understand the hard probes in hadronic collisions, including
the Higgs discovery at the LHC. In this talk, I will discuss how can
the QCD factorization help extract the same parton distribution and
correlation functions from various “lattice cross sections” – hadron
matrix elements that can be systematically calculated by using lattice
QCD techniques. With the ab initio lattice QCD calculations,
complementary to the experimental measurements, I argue that we are
entering a new era of exploring hadron’s internal structure in terms
of the dynamics of quarks and gluons.