Kälin Gregor, Liu Zhengwen, Porto Rafael A
SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA.
Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany.
Phys Rev Lett. 2020 Dec 31;125(26):261103. doi: 10.1103/PhysRevLett.125.261103.
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 et al. [Phys. Rev. Lett. 122, 201603 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.201603; J. High Energy Phys. 10 (2019) 206JHEPFG1029-847910.1007/JHEP10(2019)206].
我们使用文献[G. Kälin和R. A. Porto，《高能物理杂志》11 (2020) 106，JHEPFG1029 - 847910.1007/JHEP11(2020)106]中引入的有效场论（EFT）方法以及文献[G. Kälin和R. A. Porto，《高能物理杂志》01 (2020) 072，JHEPFG1029 - 847910.1007/JHEP01(2020)072；《高能物理杂志》02 (2020) 120，JHEPFG1029 - 847910.1007/JHEP02(2020)120]中建立的边界到边界字典，将无自旋双星的保守动力学推导至后闵可夫斯基三阶。主要要素是散射角，我们通过费曼图将其计算到(O(G^{3}))阶。通过采用振幅程序中的强大工具来适应EFT框架，我们展示了如何通过微分方程将相关的（主）积分自洽地推导到速度的所有阶次。值得注意的是，边界条件可以简化为后牛顿源的EFT中出现的相同积分。为了进行比较，我们重构了哈密顿量和散射振幅的经典极限。我们的结果与Bern等人[《物理评论快报》122, 201603 (2019)，PRLTAO0031 - 900710.1103/PhysRevLett.122.201603；《高能物理杂志》10 (2019) 206，JHEPFG1029 - 847910.1007/JHEP10(2019)206]的结果完全一致。
