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<p>Parton distribution functions (PDFs) at large <i>x</i> are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum <i>P</i><sup><i>z</i></sup> expansion of lattice quasi-PDFs, we investigate large <i>x</i> PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum <i>xP</i><sup>z</sup>, and the threshold soft function, associated with the spectator momentum (1 − <i>x</i>)<i>P</i><sup>z</sup>. The renormalization group equation of the soft function enables the resummation of the threshold double logarithms <i>α</i><sup><i>k</i></sup> ln<sup>2<i>k</i></sup>(1 − <i>x</i>), which is crucial for a reliable and controllable calculation of large <i>x</i> PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − <i>x</i>)<i>P</i><sup><i>z</i></sup> approaches Λ<sub>QCD</sub>, but remains valid when both <i>xP</i><sup><i>z</i></sup> and (1 − <i>x</i>)<i>P</i><sup><i>z</i></sup> are much larger than Λ<sub>QCD</sub>. Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.</p>

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Effects of threshold resummation for large-x PDF in large momentum effective theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月6日

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  • Xiangdong Ji,
  • Yizhuang Liu,
  • Yushan Su,
  • Rui Zhang

摘要

Parton distribution functions (PDFs) at large x are challenging to extract from experimental data, yet they are essential for understanding hadron structure and searching for new physics beyond the Standard Model. Within the framework of the large momentum Pz expansion of lattice quasi-PDFs, we investigate large x PDFs, where the matching coefficient is factorized into the hard kernel, related to the active quark momentum xPz, and the threshold soft function, associated with the spectator momentum (1 − x)Pz. The renormalization group equation of the soft function enables the resummation of the threshold double logarithms αk ln2k(1 − x), which is crucial for a reliable and controllable calculation of large x PDFs. Our analysis with pion valence PDFs indicates that perturbative matching breaks down when the spectator momentum (1 − x)Pz approaches ΛQCD, but remains valid when both xPz and (1 − x)Pz are much larger than ΛQCD. Additionally, we incorporate leading renormalon resummation within the threshold framework, demonstrating good perturbative convergence in the region where both spectator and active quark momenta are perturbative scales.