Lattice quasi-PDFs: renormalization and continuum limit

The calculation of parton distribution functions (PDFs) using lattice QCD has been revitalized in recent years thanks to new ideas such as the quasi-PDF method. The latter uses matrix elements of a nonlocal operator containing a Wilson line. At large hadron momentum, these are related to PDFs by factorization. One of the obstacles for this method was understanding how to renormalize the nonlocal operator, which is power divergent. I will discuss how using an auxiliary field allows the operator to be understood as a pair of local operators, which can be studied using standard methods. I will go on to illustrate the quasi-PDF method using a recent calculation investigating discretization effects and the approach to the continuum limit.