# Perturbative Renormalization of quasi-PDFs

## TL;DR

This paper calculates the one-loop renormalization of gauge-invariant nonlocal fermion operators with Wilson lines in lattice QCD, addressing divergences, operator mixing, and proposing non-perturbative methods for divergence subtraction.

## Contribution

It provides the first detailed one-loop lattice perturbation theory analysis of nonlocal fermion operators with Wilson lines, including mixing and divergence removal techniques.

## Key findings

- Calculated finite mixing coefficients for operator subsets.
- Identified linear and logarithmic divergences in renormalization.
- Proposed non-perturbative methods to subtract divergences.

## Abstract

In this paper we present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one-loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such long-link operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. On the lattice there is also mixing among certain subsets of these nonlocal operators; we calculate the corresponding finite mixing coefficients, which are necessary in order to disentangle individual matrix elements for each operator from lattice simulation data. Finally, extending our perturbative setup, we present non-perturbative prescriptions to extract the linearly divergent contributions.