Abstract: Recent years have seen significant progress in the lattice QCD calculation of parton physics, especially in the collinear parton distribution functions (PDFs), thanks to new methods proposed to overcome the sign problem of simulating real-time lightcone dynamics on a Euclidean lattice. Among them, the large-momentum effective theory (LaMET) has enabled much of the progress towards calculating all the 3D parton structures of the proton. The LaMET approach is an effective theory expansion of a Euclidean observable, where the accuracy of calculation is controlled by the power suppression by the large hadron momentum, and the perturbative matching of the leading-power contribution.

In this talk, I will focus on the frontier issues regarding the renormalization, higher-oder correction, resummation and power corrections, and show how to achieve a systematically controlled calculation of the PDF in lattice QCD.