Fevola Claudia, Mizera Sebastian, Telen Simon
Université Paris-Saclay, Inria, 91120 Palaiseau, France.
Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, USA.
Phys Rev Lett. 2024 Mar 8;132(10):101601. doi: 10.1103/PhysRevLett.132.101601.
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 nonplanar QCD process with multiple mass scales.
我们以一种可实际应用于维数正规化中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。在强调了教科书对朗道奇点处理中的问题之后，我们利用计算代数几何技术开发了一种对其进行分类和计算的算法。我们引入了一个称为主朗道行列式的代数簇，它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。我们针对114个示例图说明了这一点，包括一个具有多个质量标度的前沿2圈5点非平面量子色动力学过程。
