Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA.
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev Lett. 2022 Apr 22;128(16):161103. doi: 10.1103/PhysRevLett.128.161103.
We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.
我们完成了保守的二体散射动力学的第四次后闵可夫斯基阶计算，即 O(G^{4})和所有速度阶次，包括广义相对论中尾效应对应的辐射贡献。与之前的计算一样，我们利用现代散射振幅程序中的强大工具，包括广义幺正性、双复制和高级多圈积分方法，并结合有效场理论。经典振幅涉及完整的椭圆积分和最高超越权为 2 的复数对数。利用振幅-作用量关系，我们直接从振幅中得到径向作用量，并与后牛顿展开中的已知重叠项匹配。
