Zvi BernJulio Parra-MartinezRadu RoibanMichael S. RufChia-Hsien ShenMikhail P. SolonMao Zeng2024-10-092024-10-092022-04-22https://scholars.lib.ntu.edu.tw/handle/123456789/721922We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G4) 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.journal article10.1103/physrevlett.128.161103