近日，加拿大理论物理研究所的Gergely Bunth及其研究团队取得一项新进展。经过不懈努力，他们成功计算NMHV在无穷远处的引力振幅。相关研究成果已于2024年8月7日在国际知名学术期刊《高能物理杂志》上发表。

本文展示了在Risager变形的z → ∞极限下，NMHV扇区中的散射方程解如何完全分解为子扇区。每个子扇区以在极限下合并的穿刺点为特征。这自然地将E(n-3, 1)解分解为由n-3个元素的划分所表征的集合，使得恰好有一个子集包含多于一个元素。研究人员给出了对于任意n，在无穷大z附近展开的解的首阶项的解析表达式。研究人员还提供了一种简单的算法，用于数值计算同一展开式中任意高阶的项。因此，人们能够仅通过围绕无穷大的展开来计算杨-米尔斯和引力振幅。

此外，研究人员提出了一种新的解析方法，用于计算n=12 NMHV树级引力振幅在无穷远处的留数，该结果与Conde和Rajabi的结果一致。事实上，研究人员给出了Cachazo-Skinner-Mason/CHY公式中每个子扇区和所有多重性的引力子振幅在1/z的首阶项的解析形式。作为全阶算法的衍生物，人们可以获取任意n在无穷远处的留数的数值，从而得到NMHV引力振幅的修正CSW（或MHV）展开。

附：英文原文

Title: Computing NMHV gravity amplitudes at infinity

Author: Belayneh, Dawit, Cachazo, Freddy, Leon, Pablo

Issue&Volume: 2024-08-07

Abstract: In this note we show how the solutions to the scattering equations in the NMHV sector fully decompose into subsectors in the z → ∞ limit of a Risager deformation. Each subsector is characterized by the punctures that coalesce in the limit. This naturally decomposes the E(n- 3, 1) solutions into sets characterized by partitions of n - 3 elements so that exactly one subset has more than one element. We present analytic expressions for the leading order of the solutions in an expansion around infinite z for any n. We also give a simple algorithm for numerically computing arbitrarily high orders in the same expansion. As a consequence, one has the ability to compute Yang-Mills and gravity amplitudes purely from this expansion around infinity. Moreover, we present a new analytic computation of the residue at infinity of the n = 12 NMHV tree-level gravity amplitude which agrees with the results of Conde and Rajabi. In fact, we present the analytic form of the leading order in 1/z of the Cachazo-Skinner-Mason/CHY formula for graviton amplitudes for each subsector and to all multiplicity. As a byproduct of the all-order algorithm, one has access to the numerical value of the residue at infinity for any n and hence to the corrected CSW (or MHV) expansion for NMHV gravity amplitudes.

DOI: 10.1007/JHEP08(2024)051

Source: https://link.springer.com/article/10.1007/JHEP08(2024)051