论文标题
五角大楼积分到尺寸调节器中的任意顺序
Pentagon integrals to arbitrary order in the dimensional regulator
论文作者
论文摘要
我们通过分析计算一环五点主积分，\ textit {五角大楼积分}，在$ d =4-2ε$时空时尺寸中，最多可在尺寸调节器中以一个偏外腿到任意顺序。主体积分的纯粹基础是为五角大楼家族构建的，具有一个外壳腿，在简化的微分方程方法中满足了单个可观的规范微分方程。相关边界项以封闭形式给出，包括一个超几何函数，可以使用\ texttt {Mathematica} package \ texttt {hypext {hypexp}在维度调节器中扩展为任意顺序。因此，人们可以根据任意先验重量的贡献群的goncharov polylogartihm来获得规范微分方程的溶液。作为一质量五角大楼家族的特殊限制，我们从纯净和普遍的先验功能方面为无质量五角大楼家族获得了完全分析的结果。对于这两个家庭，我们都可以根据Goncharov polylogartihms提供明确的解决方案，最高四个。
We analytically calculate one-loop five-point Master Integrals, \textit{pentagon integrals}, with up to one off-shell leg to arbitrary order in the dimensional regulator in $d=4-2ε$ space-time dimensions. A pure basis of Master Integrals is constructed for the pentagon family with one off-shell leg, satisfying a single-variable canonical differential equation in the Simplified Differential Equations approach. The relevant boundary terms are given in closed form, including a hypergeometric function which can be expanded to arbitrary order in the dimensional regulator using the \texttt{Mathematica} package \texttt{HypExp}. Thus one can obtain solutions of the canonical differential equation in terms of Goncharov Polylogartihms of arbitrary transcendental weight. As a special limit of the one-mass pentagon family, we obtain a fully analytic result for the massless pentagon family in terms of pure and universally transcendental functions. For both families we provide explicit solutions in terms of Goncharov Polylogartihms up to weight four.
