论文标题
Cutkosky的大规模单环Feynman积分定理 - 第1部分
Cutkosky's Theorem for Massive One-Loop Feynman Integrals -- Part 1
论文作者
论文摘要
我们制定并证明了Cutkosky的定理，内容涉及在大规模的单循环中，直到涉及的交叉点指数中的Feynman积分的不连续性。这是通过应用技术来处理\ cite {app-iso}中开发的单数积分来完成的。我们将一环积分写为紧凑型循环中全态形式的全态家族的组成部分。然后，我们确定在哪些点发生简单的捏合，并明确计算相应消失的球体的代表。这也产生了一种算法来计算一环图的Landau表面，而无需明确求解Landau方程。我们还详细讨论了气泡，三角形和框图。
We formulate and prove Cutkosky's Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in \cite{app-iso}. We write one-loop integrals as an integral of a holomorphic family of holomorphic forms over a compact cycle. Then, we determine at which points simple pinches occur and explicitly compute a representative of the corresponding vanishing sphere. This also yields an algorithm to compute the Landau surface of a one-loop graph without explicitly solving the Landau equations. We also discuss the bubble, triangle and box graph in detail.
