Radiative contribution to classical gravitational scattering at the third order in G

Working within the post-Minkowskian approach to general relativity, we prove that the radiation-reaction to the emission of gravitational waves during the large-impact-parameter scattering of two (classical) point masses modifies the conservative scattering angle by an additional contribution of order G^3 which involves a high-energy (or massless) logarithmic divergence of opposite sign to the one contained in the third-post-Minkowskian result of Bern et al. Phys. Rev. Lett. 122, 201603 (2019). The high-energy limit of the resulting radiation-reaction-corrected (classical) scattering angle is finite, and is found to agree with the one following from the (quantum) eikonal-phase result of Amati et al. Nucl. Phys. B347, 550 (1990).