Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
Zvi Bern (Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA); Clifford Cheung (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125); Radu Roiban (Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA); Chia-Hsien Shen (Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA); Mikhail P. Solon (Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125); et al - Show all 6 authors
We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order and find agreement with known results.
