标题： 通过费曼图理解有序树幅度的零点和分裂 显示英文标题

标题： Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams

摘要： 本文中，我们利用费曼图提出对于最近发现的隐藏零点和新颖分裂的新理解。 研究重点是三个理论的有序树级振幅，这三个理论分别是 ${\rm Tr}(\phi^3)$、杨-米尔斯理论和非线性sigma模型。 我们发现了切割费曼图的三种普适方法，这些方法适用于任意图，使我们可以将完整的振幅分割为两部分或三部分。 如将展示的那样，第一种切割导致隐藏零点，第二种产生 $2$-分裂，而第三种对应于称为平滑分裂的 $3$-分裂。 在本工作中，我们频繁使用将所得片段视为正交空间的辅助技术。 然而，最终结果独立于这一辅助图像。 显示英文摘要

摘要： In this paper, we propose new understandings for recently discovered hidden zeros and novel splittings, by utilizing Feynman diagrams. The study focus on ordered tree level amplitudes of three theories, which are ${\rm Tr}(\phi^3)$, Yang-Mills, and non-linear sigma model. We find three universal ways of cutting Feynman diagrams, which are valid for any diagram, allowing us to separate a full amplitude into two/three pieces. As will be shown, the first type of cuttings leads to hidden zeros, the second one gives rise to $2$-splits, while the third one corresponds to $3$-splits called smooth splittings. Throughout this work, we frequently use the helpful auxiliary technic of thinking the resulting pieces as in orthogonal spaces. However, final results are independent of this auxiliary picture.