论文标题
主积分的重新召集方法
Resummation methods for Master Integrals
论文作者
论文摘要
我们详细介绍了从简化的微分方程方法的应用到主积分的规范基础的两种重新召集方法。第一个是一种允许轻松确定边界条件的方法，因为它找到了基本元素的边界之间的关系，而第二种方法指示了如何使用$ x \ rightarrow 1 $限制规范基础的解决方案，因此可以为同一问题提供较少质量的规范基础的解决方案。两种方法都使用了规范微分方程的字母$ \ {0,1 \} $的残基矩阵。作为概念证明，我们将这些方法应用于具有外部质量外壳的三环梯子盒的规范基础，随后获得了无质量的三环梯子及其解决方案的规范基础。
We present in detail two resummation methods emerging from the application of the Simplified Differential Equations approach to a canonical basis of master integrals. The first one is a method which allows for an easy determination of the boundary conditions, since it finds relations between the boundaries of the basis elements and the second one indicates how using the $x \rightarrow 1$ limit to the solutions of a canonical basis, one can obtain the solutions to a canonical basis for the same problem with one mass less. Both methods utilise the residue matrices for the letters $\{0,1\}$ of the canonical differential equation. As proof of concept, we apply these methods to a canonical basis for the three-loop ladder-box with one external mass off-shell, obtaining subsequently a canonical basis for the massless three-loop ladder-box as well as its solution.
