标题： 关于多回路高多重性费曼积分的有限基拓扑 显示英文标题

标题： On the finite basis topologies for multi-loop high-multiplicity Feynman integrals

摘要： 在本工作中，我们系统地分析了`t Hooft-Veltman方案中的费曼积分。我们将高多重性被积函数通过部分分式分解显式地约简为任意给定环序下的有限基底拓扑结构。我们在四外部维度下找到了所有这些有限基底拓扑结构。它们的最大切割和主要奇点都用Gram行列式和Baikov多项式来表示。通过对其中一个拓扑结构的数值探测进行无任何切割约束的分部积分约简，我们表明与传统维数正则化方案相比，计算复杂度显著降低。形式上，我们的工作意味着在微扰量子场论中每个环序的迭代积分解中出现的特殊函数的刚性有一个上限。从现象学角度看，我们提出的被积函数层级约简将大大简化为未来高多重性对撞机可观测量提供高精度预测的任务。 显示英文摘要

摘要： In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop order. We find all of these finite basis topologies at two loops in four external dimensions. Their maximal cut and the leading singularity are expressed in terms of the Gram determinant and Baikov polynomial. By performing an Integration-By-Parts reduction without any cut constraint on a numerical probe for one of these topologies, we show that the computational complexity drops significantly compared to the Conventional Dimensional Regularization scheme. Formally, our work implies an upper bound on the rigidity of special functions appearing in the iterated integral solutions at each loop order in perturbative Quantum Field Theory. Phenomenologically, the integrand-level reduction we present will substantially simplify the task of providing high-precision predictions for future high-multiplicity collider observables.