This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices as the Higgs sector of the Standard Model. Several amplitudes are considered with two, three, and four external legs. Some of them diverge in the ultraviolet region and we demonstrate that the method works in that case. It is shown that all these classes of amplitudes can be generated by four master topologies. The results of a numerical evaluation for some kinematics are presented; they are compared to public software and agree well within the error bars quoted by the different programs.

中文翻译：

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具有 I 个内部行的双循环标量函数，$I \le 5$

本文展示了混合解析/数值方法的概念证明，该方法在以前的出版物中提出，用于计算具有多达 5 个大规模传播子的标量理论中的双环函数，该标量理论具有三腿和四腿顶点作为希格斯扇区标准型号。使用两个、三个和四个外部腿来考虑几个幅度。其中一些在紫外线区域发散，我们证明该方法在这种情况下有效。结果表明，所有这些类别的幅度都可以由四个主拓扑生成。给出了一些运动学的数值评估结果；将它们与公共软件进行比较，并且在不同程序引用的误差范围内非常一致。