Numerical evaluation of loop integrals
Numerical evaluation of loop integrals
复制标题
循环积分的数值计算
DOI：
10.1088/1126-6708/2006/10/031
复制
发表时间：
2005
影响因子：
5.4
通讯作者：
A. Daleo
中科院分区：
文献类型：
--
作者：
C. Anastasiou;A. Daleo
本文提出了一维正则化中任意环积分数值求值的一种新方法。我们首先推导了Mellin-Barnes积分表示，并应用基于柯西定理的算法技术提取了ε ->极限的发散部分。然后我们进行了一个展开，并数值计算了展开的积分系数。该方法在物理运动区域产生稳定的结果，避免了复杂的解析延拓。它也可以应用于计算标量积分和张量积分而不使用约简方法。我们用具有许多运动尺度的红外发散积分的具体例子来证明我们的方法，例如双环和三环盒积分以及单环六边形拓扑的六阶张量积分。
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.