Numerical reconstruction techniques are widely employed in the calculation of multiloop scattering amplitudes. In recent years, it has been observed that the rational functions in multiloop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a $p$-adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of the rank-5 integrals appearing in two-loop five-point full-color massless amplitude calculations in quantum chromodynamics. The number of required numerical probes (per prime field) is found to be around 25 times smaller than in conventional techniques, and the obtained result is 130 times smaller. The reconstructed result displays signs of additional structure that could be used to further reduce its size and the number of required probes.

中文翻译：

---

多环振幅中有理函数的 p 进重构


数值重建技术被广泛应用 $p$ 致力于多环散射振幅的计算。近年来，人们发现多循环计算中的有理函数在部分分式下大大简化。在本文中，我们提出了一种直接以部分分式形式重构有理函数的技术，通过在 p 进度量下根据其属性选择的特殊整数点来评估函数。作为一种应用，我们应用这种技术来重建量子色动力学中出现在两环五点全色无质量振幅计算中的五阶积分之一的分部积分简化中的最大有理函数。发现所需的数值探针数量（每个素数字段）比传统技术少约 25 倍，并且获得的结果小 130 倍。重建结果显示出额外结构的迹象，可用于进一步减小其尺寸和所需探针的数量。