论文标题
用退化的革兰氏矩阵减少一环积分
Reduction with Degenerate Gram matrix for One-loop Integrals
论文作者
论文摘要
在\ cite {feng：2021enk，hu：2021nia}中提出了一种使用辅助矢量$ r $的一环积分的PV还原方法。还已经证明了新方法是\ cite {feng：2022uqp}中的一种自我完成的方法。在这种方法中，递归关系可以很容易地产生分析还原系数，在该方法中，革兰氏决定因素出现在分母中。克决定因素引起的奇异性是一个众所周知的事实，在给定框架中解决这些分歧很重要。在本文中，我们提出了一种系统的算法来解决我们方法中的这个问题。关键的想法是，现在，最高拓扑的主体积分将被分解为较低拓扑的主积分的组合。通过要求取消差异以获得一般还原系数，我们将分解系数作为泰勒的泰勒级数序列。此外，相同的想法可以应用于其他差异。
An improved PV-reduction method for one-loop integrals with auxiliary vector $R$ has been proposed in \cite{Feng:2021enk,Hu:2021nia}. It has also been shown that the new method is a self-completed method in \cite{Feng:2022uqp}. Analytic reduction coefficients can be easily produced by recursion relations in this method, where the Gram determinant appears in denominators. The singularity caused by Gram determinant is a well-known fact and it is important to address these divergences in a given frame. In this paper, we propose a systematical algorithm to deal with this problem in our method. The key idea is that now the master integral of the highest topology will be decomposed into combinations of master integrals of lower topologies. By demanding the cancellation of divergence for obtained general reduction coefficients, we solve decomposition coefficients as a Taylor series of the Gram determinant. Moreover, the same idea can be applied to other kinds of divergences.
