论文标题
使用辅助矢量减少日落拓扑的PV减少
PV-Reduction of Sunset Topology with Auxiliary Vector
论文作者
论文摘要
事实证明，Passarino-Veltman（PV）还原方法对于一般的单环积分的计算非常有用。但是，应用于较高的循环时并没有取得太大进展。最近，我们通过引入辅助向量改善了PV还原方法。在本文中，我们将新方法应用于最简单的两环积分，即日落拓扑。我们展示了如何使用差分运算符来建立代数递归关系以减少系数。我们的算法可以轻松地应用于使用任意高量张量结构的积分的减少。我们通过计算降低的总张量排名高达四个来证明算法的效率。
Passarino-Veltman (PV) reduction method has been proved to be very useful for the computation of general one-loop integrals. However, not much progress has been made when applying to higher loops. Recently, we have improved the PV-reduction method by introducing an auxiliary vector. In this paper, we apply our new method to the simplest two-loop integrals, i.e., the sunset topology. We show how to use differential operators to establish algebraic recursion relations for reduction coefficients. Our algorithm can be easily applied to the reduction of integrals with arbitrary high-rank tensor structures. We demonstrate the efficiency of our algorithm by computing the reduction with the total tensor rank up to four.
