Comments on "Non-local Nucleon Matrix Elements in the Rest Frame"

TL;DR

This paper critiques a recent study on non-local nucleon matrix elements, arguing that perturbative QCD is invalid at the studied distance scales and that the proposed Gaussian correction does not justify its use.

Contribution

It provides a critical analysis of the previous work's methodology, highlighting the breakdown of perturbative QCD at certain distances and questioning the validity of the Gaussian correction model.

Findings

Perturbative QCD breaks down at distances above 0.3 fm.

The ansatz used in the previous study fails to fit data beyond 0.3 fm.

Gaussian correction reduces discrepancies but does not justify perturbative methods.

Abstract

In a recent paper, "Non-local Nucleon Matrix Elements in the Rest Frame" (Phys. Rev. D 111, 5 (2025)), it was observed that the next-to-leading order calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. We argue that perturbative QCD breaks down at such a distance scale after resumming the associated large logarithms, while the ansatz used in the analysis there is not justified in perturbation theory. Besides, we explain the observation in Phys. Rev. D 111, 5 (2025) and demonstrate that the ansatz fails to describe the data for $z>0.3$ fm, showing an opposite trend. Finally, although Phys. Rev. D 111, 5 (2025) proposes multiplying the ansatz by a Gaussian correction model, which is shown to reduce the discrepancy with the data, this does not legitimize the use of perturbative QCD at such distance scales.