物理
标量(数学)
Slater积分
维数正则化
体积积分
正规化(语言学)
运动学
循环(图论)
张量(固有定义)
秩(图论)
费曼积分
积分阶(微积分)
应用数学
数学分析
纯数学
数学物理
数学
积分方程
重整化
经典力学
几何学
量子力学
计算机科学
人工智能
组合数学
费曼图
作者
Charalampos Anastasiou,Alejandro Daleo
标识
DOI:10.1088/1126-6708/2006/10/031
摘要
We present a new method for the numerical evaluation of arbitrary loop integrals in dimensional regularization. We first derive Mellin-Barnes integral representations and apply an algorithmic technique, based on the Cauchy theorem, to extract the divergent parts in the epsilon->0 limit. We then perform an epsilon-expansion and evaluate the integral coefficients of the expansion numerically. The method yields stable results in physical kinematic regions avoiding intricate analytic continuations. It can also be applied to evaluate both scalar and tensor integrals without employing reduction methods. We demonstrate our method with specific examples of infrared divergent integrals with many kinematic scales, such as two-loop and three-loop box integrals and tensor integrals of rank six for the one-loop hexagon topology.
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