Top-forms of leading singularities in nonplanar multi-loop amplitudes
Top-forms of leading singularities in nonplanar multi-loop amplitudes
复制标题
DOI：
10.1140/epjc/s10052-018-5629-z
复制
发表时间：
2015-06
期刊：
影响因子：
--
通讯作者：
Baoyi Chen;Gang Chen;Y. E. Cheung;Ruofei Xie;Yuan Xin
中科院分区：
文献类型：
--
作者：
Baoyi Chen;Gang Chen;Y. E. Cheung;Ruofei Xie;Yuan Xin
在壳图是研究散射振幅的重要工具。本文讨论了无外BCFW桥的壳上图。我们引入了一个额外的步骤，添加一个辅助的外部动量线。然后，我们可以通过移除外部BCFW桥来分解壳上图，从而将其分解为平面图，该平面图的顶形式现在是众所周知的。具有辅助线的壳上图的顶部形式可以通过按照我们之前的论文中所讨论的相反顺序添加BCFW桥来获得（Chen等人，Eur Phys J C 77（2）：80 2017）。为了得到原始图形的顶形，需要对辅助线进行软限幅。得到了格拉斯曼积分的演化规律和软极限下的几何约束。这就完成了对超杨米尔斯（SYM）非平面散射振幅中主导奇点的顶式描述，该描述适用于任意高阶环和超出最大螺旋度破坏（MHV）振幅的情形.
The on-shell diagram is a very important tool in studying scattering amplitudes. In this paper we discuss the on-shell diagrams without external BCFW bridges. We introduce an extra step of adding an auxiliary external momentum line. Then we can decompose the on-shell diagrams by removing external BCFW bridges to a planar diagram whose top-form is well known now. The top-form of the on-shell diagram with the auxiliary line can be obtained by adding the BCFW bridges in an inverse order as discussed in our former paper (Chen et al. in Eur Phys J C 77(2):80 2017). To get the top-form of the original diagram, the soft limit of the auxiliary line is needed. We obtain the evolution rule for the Grassmannian integral and the geometry constraint in the soft limit. This completes the top-form description of leading singularities in nonplanar scattering amplitudes ofSuper Yang–Mills (SYM), which is valid for arbitrary higher-loops and beyond the Maximally-Helicity-Violation (MHV) amplitudes.