AI 中文总结
本文综述梯度流作为QCD紫外正则化方法在算子乘积展开中的精确转换性质，及其在部分子分布、重介子、夸克质量和强耦合定义中的应用，并涉及量子引力中Ricci流的研究。
AI 中文摘要
梯度流为QCD提供了一种规范不变且O(4)不变的紫外正则化方法。这为将非微扰格点计算与微扰结果相结合开辟了新的机遇，尤其是在算子乘积展开（OPE）的背景下。我们回顾了其背后的概念，并论证在给定OPE的算子基内，流动的Wilson系数与常规Wilson系数之间的转换对流动时间的依赖在每个微扰阶都是精确的。本文讨论了在部分子分布函数、重介子观测量、夸克质量以及强耦合的梯度流定义方面的近期应用。最后，综述了量子引力中Ricci流的微扰表述及其在非高斯不动点研究中的应用。
英文摘要
The gradient flow provides a gauge- and O(4)-invariant ultraviolet regulator for QCD. This opens new opportunities for combining non-perturbative lattice calculations with perturbative results, in particular in the context of an operator-product expansion (OPE). We review the concepts behind this and argue that, within the operator basis of a given OPE, the flow-time dependence of the conversion between flowed and regular Wilson coefficients is exact at each perturbative order. Recent applications to parton distribution functions, heavy-meson observables, quark masses, and gradient-flow definitions of the strong coupling are discussed. Finally, the perturbative formulation of the Ricci flow in quantum gravity and its application to the study of non-Gaussian fixed points is reviewed.
Comments17 pages, 2 figures; talk presented at Loops and Legs in Quantum Field Theory 2026
