论文标题
从五环散射幅度到用环状双重性打开树木
From five-loop scattering amplitudes to open trees with the Loop-Tree Duality
论文作者
论文摘要
表征Multiloop拓扑是在量子场理论中高扰动阶以开发新方法的重要步骤。在本文中，我们利用环状双重性（LTD）形式主义分析了在五个循环中首次出现的多旋转拓扑。明确地，我们将循环打开到连接的树木中，并根据其拓扑特性进行分组。然后，我们确定了一个内核发生器，即所谓的N $^7 $ MLT通用拓扑，该拓扑使我们能够描述最多五个循环的任何散射幅度。此外，我们提供分解和递归关系，使我们能够以更简单的子接头来编写这些多核拓扑，包括几个具有任意循环数量的Feynman图的子集。我们的方法利用了原始五环拓扑的图形描述中存在的许多对称性。本文中获得的结果可能会阐明对运行耦合的高阶校正的更有效的确定，这对于当前和将来的精度物理计划至关重要。
Characterizing multiloop topologies is an important step towards developing novel methods at high perturbative orders in quantum field theory. In this article, we exploit the Loop-Tree Duality (LTD) formalism to analyse multiloop topologies that appear for the first time at five loops. Explicitly, we open the loops into connected trees and group them according to their topological properties. Then, we identify a kernel generator, the so-called N$^7$MLT universal topology, that allow us to describe any scattering amplitude of up to five loops. Furthermore, we provide factorization and recursion relations that enable us to write these multiloop topologies in terms of simpler subtopologies, including several subsets of Feynman diagrams with an arbitrary number of loops. Our approach takes advantage of many symmetries present in the graphical description of the original fundamental five-loop topologies. The results obtained in this article might shed light into a more efficient determination of higher-order corrections to the running couplings, which are crucial in the current and future precision physics program.
