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Comment on “Nonlocal nucleon matrix elements in the rest frame”

Xiang Gao1, Jinchen He2,1, Yushan Su2, Rui Zhang1, and Yong Zhao1

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Phys. Rev. D 113, 018501 – Published 26 January, 2026

DOI: https://doi.org/10.1103/gbnw-9zrt

Abstract

In a recent paper, “Nonlocal nucleon matrix elements in the rest frame” [1], 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 quantum chromodynamics (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 Ref. [1] and demonstrate that the Ansatz fails to describe the data for z>0.3  fm, showing an opposite trend. Finally, although Ref. [1] 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.

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Original Article

Nonlocal nucleon matrix elements in the rest frame

Joe Karpie, Christopher Monahan, and Anatoly Radyushkin
Phys. Rev. D 111, 054503 (2025)

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Information

Phys. Rev. D 113, 018501– Published 26 January, 2026
  • Received 9 May 2025
  • Accepted 6 August 2025
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