英国赫特福德大学Ross Glew团队研究了循环空间中的正阶梯和负阶梯。该项研究成果发表在2025年6月12日出版的《高能物理杂志》上。

基于N=4超杨米尔斯（SYM）中散射振幅的双环MHV被积函数的新项分解公式，以及环空间中五点负阶梯的最新结果，研究组给出了任意数量粒子到所有环的环空间中一般阶梯的规范形式。他们使用了负几何文献中引入的图形符号，其中每个环动量表示为一个顶点，相互正性（或负性）条件表示为正（或负）边。 

研究组扩展了这个符号，以包括单环动量放大面体的腔室的概念。配备了这种新的图形符号，他们找到了所有MHVn振幅的L环（负/正）阶梯的规范形式。这种最终公式非常简单，让人想起单环和双环动量放大面体的手性五边形展开。它将阶梯贡献表示为最大割上的和，每个项都出现在和因子分解成手性五边形或其简单推广的乘积中。

附：英文原文

Title: Positive and negative ladders in loop space

Author: Glew, Ross, ukowski, Tomasz

Issue&Volume: 2025-06-12

Abstract: Motivated by a new term-wise factorised formula for the two-loop MHV integrand for scattering amplitudes in N=4 super Yang-Mills (SYM), together with recent results for the five-point negative ladders in loop space, we present the canonical forms for general ladders in loop space for an arbitrary number of particles to all loops. We make use of the graphical notation introduced in the negative geometries literature, where each loop momentum is represented as a vertex, and mutual positivity (resp. negativity) conditions as a positive (resp. negative) edge. In this paper we extend this notation to include the notion of chambers of the one-loop momentum amplituhedron. Equipped with this new graphical notation, we find the canonical form of the L-loop (negative/positive) ladders for all MHVn amplitudes. Our final formula is remarkably simple and reminiscent of the chiral pentagon expansion of the one and two loop momentum amplituhedron. It expresses ladder contributions as sums over maximal cuts, with each term appearing in the sum factorising into products of either chiral pentagons or their simple generalisations.

DOI: 10.1007/JHEP06(2025)124

Source: https://link.springer.com/article/10.1007/JHEP06(2025)124