标题： 具有三个质量顶点的一环六维六边形积分 显示英文标题

标题： The one-loop six-dimensional hexagon integral with three massive corners

摘要： 我们用三个非相邻外部质量对六维六边形积分进行解析计算。 经过简单的缩放，它由六个对偶共形不变的交叉比函数给出。 结果可以表示为24项的和，这些项只涉及一个基本函数，该函数是具有统一三重超越度的对数、双对数和三对数的简单线性组合。 我们的方法使用微分方程来确定该函数的符号，并使用一个算法从其符号中重建该函数。 已知六维六边形积分与N=4超杨-米尔斯理论中的散射振幅密切相关，因此我们期望我们的结果有助于理解该理论中散射振幅的结构，尤其是在两环情况下。 显示英文摘要

摘要： We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N=4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.