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  • Open Access

Lattice-QCD Computable Quark Correlation Functions at Three-Loop Order and Extraction of Splitting Functions

Chen Cheng*, Li-Hong Huang†, and Xiang Li‡

Zheng-Yang Li§

Yan-Qing Ma1,∥

  • Theory Center, Jefferson Lab, 12000 Jefferson Avenue, Newport News, Virginia 23606, USA

  • School of Physics, Peking University, Beijing 100871, China and Center for High Energy Physics, Peking University, Beijing 100871, China

  • *Contact author: 1801214966@pku.edu.cn
  • †Contact author: lhhuang@pku.edu.cn
  • ‡Contact author: lix-PHY@pku.edu.cn
  • §Contact author: zyli@jlab.org
  • ∥Contact author: yqma@pku.edu.cn
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Phys. Rev. Lett. 134, 251902 – Published 24 June, 2025

DOI: https://doi.org/10.1103/53ys-3n19

Abstract

We present the first complete next-to-next-to-next-to-leading-order calculation of the matching coefficients that link unpolarized flavor nonsinglet parton distribution functions with lattice QCD computable correlation functions. By using this high-order result, we notice a reduction in theoretical uncertainties compared to relying solely on previously known lower-order matching coefficients. Furthermore, based on this result we have extracted the three-loop unpolarized flavor nonsinglet splitting function, which is in agreement with the state-of-the-art result. Because of the simplicity of our method, it has the potential to advance the calculation of splitting functions to the desired four-loop order.

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Phys. Rev. Lett. 134, 251902– Published 24 June, 2025
  • Received 6 November 2024
  • Revised 16 May 2025
  • Accepted 30 May 2025
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