格点量子色动力学（QCD）给出的部分子分布函数
Parton distribution functions from lattice QCD
AI总结：
本研究介绍基于空间非定域矩阵元的现代格点QCD方法，解决光锥关联与欧几里得时空的差异问题，计算质子、π介子等的部分子分布函数，助力强子部分子结构研究。
AI中文摘要：
部分子分布函数（PDFs）是描述量子色动力学（QCD）中强子部分子结构最直接的方式之一，它们编码了夸克、反夸克和胶子关于部分子动量分数$x$的非微扰信息，并通过QCD因子化将这种微观结构与实验可测量的高能散射过程关联起来，这使得用格点QCD研究PDFs颇具吸引力，格点QCD提供了强相互作用的第一性原理表述。难点在于PDFs通过光锥关联定义，而格点QCD建立在欧几里得时空之上。本章介绍了格点QCD计算PDFs的理论基础与当前状态，重点关注基于空间非定域矩阵元的现代方法。我们首先回顾夸克和胶子PDFs的光锥定义、其Mellin矩以及与QCD因子化的关联；随后解释大动量有效理论、短距离因子化和短距离算符乘积展开如何将欧几里得格点观测量与光锥部分子结构关联起来。特别关注了过去五年间取得进展的要素：Wilson线算符的重整化、微扰匹配、有限动量和有限距离效应、$x$依赖的重建以及系统不确定性。我们总结了质子夸克PDFs、π介子和K介子PDFs、胶子PDFs以及 twist-3 分布的选定格点结果，强调了近期进展与剩余挑战。正如将要展示的，格点QCD正从原理验证计算向可系统改进的确定方法迈进，这种方法可补充实验数据和全局QCD分析，用于绘制强子的部分子结构图谱。
英文摘要：
Parton distribution functions (PDFs) provide one of the most direct ways to describe the partonic structure of hadrons in QCD. They encode nonperturbative information about quarks, antiquarks, and gluons as functions of the partonic momentum fraction $x$, and they connect this microscopic structure to experimentally measurable high-energy scattering processes through QCD factorization. This makes PDFs interesting to pursue with lattice QCD, which provides a first-principles formulation of the strong interaction. The challenge is that PDFs are defined through light-cone correlations, while lattice QCD is formulated in Euclidean spacetime. This chapter introduces the theoretical foundations and current status of lattice-QCD calculations of PDFs, with emphasis on modern approaches based on spatially nonlocal matrix elements. We first review the light-cone definitions of quark and gluon PDFs, their Mellin moments, and the connection to QCD factorization. We then explain how large-momentum effective theory, short-distance factorization, and the short-distance operator product expansion make it possible to relate Euclidean lattice observables to light-cone partonic structure. Particular attention is given to the elements that have improved over the last five years: renormalization of Wilson-line operators, perturbative matching, finite-momentum and finite-distance effects, reconstruction of the $x$ dependence, and systematic uncertainties. We summarize selected lattice results for proton quark PDFs, pion and kaon PDFs, gluon PDFs, and twist-3 distributions, highlighting both recent progress and remaining challenges. As will be demonstrated, lattice QCD is moving from proof-of-principle calculations toward systematically improvable determinations that can complement experimental data and global QCD analyses in mapping the partonic structure of hadrons.
