Even since the "quasi" parton distribution function (PDF) was proposed under the large-momentum effective theory (LaMET) framework, its renormalization under the lattice regularization has been a central challenge to be solved due to the linear divergence. Thus, we investigate several possible ways to renormalize the quasi-PDF operators in high accuracy with non-perturbative calculation using the quench configurations at several lattice spacings. We find that the ratio of the UV divergences obtained from the Wilson loop and off-shell quasi-PDF operator is not a constant of the Wilson link length z. Although the linear divergence in them may be consistent to each other numerically, there is some additional UV divergence in the quasi-PDF operator.
@article{arxiv.1912.06056,
title = {UV divergence of the quasi-PDF operator under the lattice regularization},
author = {Yikai Huo and Peng Sun},
journal= {arXiv preprint arXiv:1912.06056},
year = {2019}
}