论文标题
大量的单循环保形feynman积分和多个超测量系列的二次变换
Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
论文作者
论文摘要
同一位作者在同伴论文中呈现的$ n $ fold Mellin-Barnes（MB）积分的计算技术用于得出各种配置中大型的一环三点Feynman积分的串联表示。这表明了该方法在非谐振情况下（通用传播功率）以及其在共振剂（单位传播功率）中的一些微妙之处的极为简单性和效率。我们确认了物理和数学文献中的某些结果，并提供了许多新的结果，其中一些涉及更通用的大型单环$ N $ - 点案例。特别是，我们证明了两个最近的猜想，这些猜想在多个超几何序列方面提供了庞大的单环$ n $ n $ n $ - 点积分（对于通用传播器）。我们展示了这些猜想是如何通过Yangian Bootstrap分析推论出来的，它是由新的二次变换塔中的高几幅函数理论中的塔楼相关的。最后，我们还使用我们的MB方法来确定扬吉方法中可能出现的虚假贡献。
The computational technique of $N$-fold Mellin-Barnes (MB) integrals, presented in a companion paper by the same authors, is used to derive sets of series representations of the massive one-loop conformal 3-point Feynman integral in various configurations. This shows the great simplicity and efficiency of the method in nonresonant cases (generic propagator powers) as well as some of its subtleties in the resonant ones (for unit propagator powers). We confirm certain results in the physics and mathematics literature and provide many new results, some of them dealing with the more general massive one-loop conformal $n$-point case. In particular, we prove two recent conjectures that give the massive one-loop conformal $n$-point integral (for generic propagator powers) in terms of multiple hypergeometric series. We show how these conjectures, that were deduced from a Yangian bootstrap analysis, are related by a tower of new quadratic transformations in Hypergeometric Functions Theory. Finally, we also use our MB method to identify spurious contributions that can arise in the Yangian approach.
