近日，美国马里兰大学的Jinchen He及其研究团队取得一项新进展。经过不懈努力，他们揭示库仑规范中部分子分布晶格法计算中格里波夫副本的系统不确定性。相关研究成果已于2024年12月20日在国际知名学术期刊《中国物理快报》上发表。

本研究评估了格里波夫副本对库仑规范固定下的夸克关联函数的影响。研究人员采用了不同的库仑规范固定策略，并基于晶格规范构型选择了两组不同的格里波夫副本。研究人员比较了真空状态和π介子状态下所得空间夸克关联函数的差异。研究结果表明，无论关联范围如何，来自两组格里波夫拷贝的矩阵元素的统计误差均随规范构型数量的平方根成比例减小。与规范噪声相比，两种策略之间的差异不具有统计显著性，这表明在实际晶格计算夸克部分子分布时，格里波夫副本的影响可以忽略不计。

据悉，近期，有研究提出了一种新方法，在大动量有效理论框架下，利用库仑规范（CG）中固定的增强型关联函数来计算部分子分布。这种方法无需使用威尔逊线，可能显著提升晶格量子色动力学计算的效率和精度。然而，关于晶格规范固定中存在的格里波夫副本所带来的系统不确定性是否得到了充分控制，仍存在担忧。

附：英文原文

Title: Systematic Uncertainties from Gribov Copies in Lattice Calculation of Parton Distributions in the Coulomb Gauge

Author:Xiang Gao^1,2, Jinchen He^3,1*, Rui Zhang¹, and Yong Zhao¹

Issue&Volume: 2024-12-20

Abstract: Recently, a new method has been proposed to compute parton distributions using boosted correlators fixed in the Coulomb gauge (CG) within the framework of large-momentum effective theory. This approach, which does not involve Wilson lines, could greatly improve the efficiency and precision of lattice quantum chromodynamics calculations. However, concerns remain regarding whether systematic uncertainties from Gribov copies, which correspond to ambiguities in lattice gauge-fixing, are adequately controlled. This work assesses the effects of Gribov copies on Coulomb-gauge-fixed quark correlators. We utilize different strategies for Coulomb-gauge fixing, selecting two different groups of Gribov copies based on lattice gauge configurations. We examine the differences in the resulting spatial quark correlators in both vacuum and pion states. Our findings indicate that the statistical errors of the matrix elements from both Gribov copies, regardless of the correlation range, decrease proportionally to the square root of the number of gauge configurations. The difference between the strategies does not show statistical significance compared to the gauge noise, demonstrating that the effect of the Gribov copies can be neglected in practical lattice calculations of quark parton distributions.

DOI: 10.1088/0256-307X/41/12/121201

Source: https://cpl.iphy.ac.cn/10.1088/0256-307X/41/12/121201