Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach.

Zhengwen Liu,Gregor Kälin,Rafael A. Porto

doi:10.1103/physrevlett.125.261103

Abstract

We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106JHEPFG1029-847910.1007/JHEP11(2020)106] together with the boundary-to-bound dictionary developed in [G. Kälin and R. A. Porto, J. High Energy Phys. 01 (2020) 072JHEPFG1029-847910.1007/JHEP01(2020)072; J. High Energy Phys. 02 (2020) 120.JHEPFG1029-847910.1007/JHEP02(2020)120]. The main ingredient is the scattering angle, which we compute to O(G^{3}) via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern etal. [Phys. Rev. Lett. 122, 201603 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.201603; J. High Energy Phys. 10 (2019) 206JHEPFG1029-847910.1007/JHEP10(2019)206].

Highlights

Introduction.—The discovery potential heralded by the new era of gravitational wave science [1,2] has motivated high-accuracy theoretical predictions for the dynamics of binary systems [3,4,5]
We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G
Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated integrals are bootstrapped to all orders in velocities via differential equations

Summary

Introduction

Introduction.—The discovery potential heralded by the new era of gravitational wave science [1,2] has motivated high-accuracy theoretical predictions for the dynamics of binary systems [3,4,5]. Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G.

Results

Conclusion