标题： 重新审视朗道奇点：费曼积分的计算代数几何 显示英文标题

标题： Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

摘要： 我们以一种可以实际应用于标准模型微扰计算的方式重新阐述了费曼积分奇点的分析。 在强调教科书中处理兰道奇点的问题后，我们开发了一种算法，使用计算代数几何技术对它们进行分类和计算。 我们引入了一个称为主兰道行列式的代数簇，即使在存在无质量粒子或紫外/红外发散的情况下也能捕捉奇点。 我们对此进行了114个示例图的说明，包括一个具有多个质量尺度的前沿二环五点非平面QCD过程。 本文介绍的算法已实现于开源Julia包PLD.jl中，可在https://mathrepo.mis.mpg.de/PLD/获取。 显示英文摘要

摘要： We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point non-planar QCD process with multiple mass scales. The algorithms introduced in this work are implemented in the open-source Julia package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.