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Regularization prescription for the mixing between nonlocal gluon and quark operators

Yao Ji1, Zhuoyi Pang1,2,*, Fei Yao3,1, and Jian-Hui Zhang1,†

  • *Contact author: Zhuoyi.Pang@ncbj.gov.pl
  • †Contact author: zhangjianhui@cuhk.edu.cn
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Phys. Rev. D 113, 014029 – Published 27 January, 2026

DOI: https://doi.org/10.1103/scjd-q4b6

Abstract

It is well known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimensional regularization resolves this issue and yields consistent results in both coordinate and momentum space. This prescription is also compatible with lattice extractions of parton distributions from nonlocal operators.

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Phys. Rev. D 113, 014029– Published 27 January, 2026
  • Received 14 October 2025
  • Accepted 7 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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