In these proceedings we present results for the renormalization of fermion bilinear operators which contain a Wilson line, to one-loop level in lattice perturbation theory. These operators are needed for the calculation of the so-called quasi-PDFs, recently proposed by X. Ji. Our calculations have been performed for a variety of formulations, including Wilson/clover fermions and a wide class of Symanzik improved gluon actions.

We focus on aspects related to the renormalization of the quasi-PDFs, which is a highly nontrivial component of their calculation. The extended nature of the Wilson-line operators results in additional divergences as compared to ultra-local currents. More precisely, there is a linear, as well as logarithmic divergence with the lattice spacing.

We demonstrate how certain operators mix in lattice regularization and we compute the finite mixing coefficients. These are necessary to disentangle individual matrix elements for each operator from lattice simulation data. Furthermore, based on our findings in the perturbative calculation, we develop a non-perturbative prescription to extract the multiplicative renormalization and mixing coefficients.