Parton distributions with lattice QCD: how it works

Exploration of parton distributions with lattice simulations is the rapidly growing field of QCD. Different collaborations use a variety of observables to study the parton dynamics, including quasi- and pseudo- parton distributions, Ioffe-time distributions, current correlators, and others. All these approaches are grounded on the same fundamental principle: QCD factorization theorems. In the talk, I describe how and why QCD factorization theorems can be applied to lattice observables. I highlight strong and weaks sides of various observables. Also, I discuss the possibility to study transverse-momentum motions of partons with lattice methods, which was suggested recently.