在$O(G^6)$的引力动力学：微扰引力散射与实验数学的相遇
Gravitational dynamics at $O(G^6)$: perturbative gravitational scattering meets experimental mathematics
摘要：
最近介绍的方法，引力动力学的二进制系统涉及复杂的积分，连接到非本地的时间相互作用产生的5圈水平的经典引力散射。我们完成了经典引力散射的分析评估在第六阶牛顿常数，$G$，并在第六后牛顿的准确性。我们使用计算技术开发的多圈费曼积分的评价，以获得我们的结果在两种方式：高精度的算术，产生重建的解析表达式，并直接集成{ \it通过}调和多项式。尾部对散射的贡献的解析表达式涉及到权重为4的超越常数。
英文摘要：
A recently introduced approach to the gravitational dynamics of binary systems involves intricate integrals, linked to nonlocal-in-time interactions arising at the 5-loop level of classical gravitational scattering. We complete the analytical evaluation of classical gravitational scattering at the sixth order in Newton's constant, $G$, and at the sixth post-Newtonian accuracy. We use computing techniques developed for the evaluation of multi-loop Feynman integrals to obtain our results in two ways: high-precision arithmetic, yielding reconstructed analytic expressions, and direct integration {\it via} Harmonic Polylogarithms. The analytic expression of the tail contribution to the scattering involve transcendental constants up to weight four.
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