论文标题
用交叉理论构建规范的Feynman积分
Constructing Canonical Feynman Integrals with Intersection Theory
论文作者
论文摘要
规范的Feynman积分在多环级别的散射幅度的研究中引起了极大的兴趣。我们建议构建超几何类型的$ d \ log $ - 形式积分，将其视为Feynman积分的表示，并使用相交理论将它们投射到主积分中。这提供了一种建立规范主积分的建设性方法，其微分方程可以轻松求解。我们使用我们的方法来研究最大剪切的积分和未切割的积分，并在一个和两个循环中研究其在多个尺度的问题中的适用性。
Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $d\log$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals, and project them into master integrals using intersection theory. This provides a constructive way to build canonical master integrals whose differential equations can be solved easily. We use our method to investigate both the maximally cut integrals and the uncut ones at one and two loops, and demonstrate its applicability in problems with multiple scales.
