UV divergence of the quasi-PDF operator under the lattice regularization

TL;DR

This paper investigates the UV divergence issues in the renormalization of quasi-PDF operators under lattice regularization, revealing additional divergences beyond linear ones and exploring non-perturbative solutions.

Contribution

It provides a detailed non-perturbative analysis of UV divergences in quasi-PDF operators and identifies challenges in their renormalization on the lattice.

Findings

The ratio of UV divergences from Wilson loop and quasi-PDF operators varies with Wilson link length.

Additional UV divergences exist in quasi-PDF operators beyond linear divergence.

Linear divergences may be numerically consistent but are not the whole story.

Abstract

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.