Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach (2007.04977v2)

Abstract: We derive the conservative dynamics of non-spinning binaries to third Post-Minkowskian order, using the Effective Field Theory (EFT) approach introduced in [2006.01184] together with the Boundary-to-Bound dictionary developed in [1910.03008, 1911.09130]. The main ingredient is the scattering angle, which we compute to ${\cal O}(G^3)$ 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. [1901.04424, 1908.01493].

Conservative Dynamics of Binary Systems via Effective Field Theory

This paper presents a rigorous exploration into the conservative dynamics of non-spinning binary systems up to third-order Post-Minkowskian (3PM) using the Effective Field Theory (EFT) framework. The primary focus is leveraging the approach to compute scattering angles and constructing the Hamiltonian pertinent to these systems, ensuring consistency with previous results by Bern et al.

Key Contributions

The authors provide a comprehensive methodology using EFT to calculate the dynamics of binary systems, emphasizing the conservative aspect devoid of radiation-reaction effects. The research builds upon previous work with Post-Newtonian (PN) expansions, adapting and optimizing modern tools from particle physics, such as Feynman diagrams and analytic methods, to derive third-order corrections in binary interactions. Through the paper's technical outline, the authors highlight:

• Scattering Angle Computation: The paper meticulously computes the scattering angle to $\mathcal{O}(G^3)$ using Feynman diagrams, with prominent accuracy, methodically matching results from previous works. This involves an intricate calculation of impulse changes during binary interactions.
• Convincing the use of EFT: The EFT framework is illuminated as a potent tool that systematically organizes calculations, particularly showcasing differential equations' role in determining master integrals' dependence on velocity. The EFT approach allows for modular calculations, emphasizing its scalability for extending such computations beyond 3PM.
• Boundary-to-Bound Dictionary Application: By applying the Boundary-to-Bound (B2B) dictionary, the authors transform scattering data to derive gauge-invariant observables analytically continued for generic orbital configurations. This approach effectively combines scattering information with bound state dynamics.

Numerical Results

The authors reveal strong numerical results demonstrating the 3PM order agreement with previous research, particularly Bern et al. Notably, they detail the impulse on the binaries and the derived scattering angle, showing correctness across computational methods, subsequently leading to expressions for Hamiltonians and classical limits of scattering amplitudes.

Implications and Speculation

The implications of this paper are profound in the field of gravitational wave science. It provides an extensive toolset for understanding small relative velocity inspirals that are pivotal in the detection and analysis phase. The potential for extending the EFT to compute higher-order corrections is apparent, speculating that future research may reach up to 5PM order by capitalizing on similar quantum field theory techniques and leveraging known PN expansions.

Future Developments

The authors suggest that the infusion of data external to conventional expansion regimes, such as test-particle limits in Schwarzschild geometries, could facilitate even greater computational simplifications and accuracy. Additionally, continuous improvements in master integral calculations might optimize the EFT approach for even higher orders, promising developments in both theoretical predictions and practical applications for gravitational wave observations.

In conclusion, this paper affirms the efficacy of EFT in studying conservative binary dynamics, giving rise to potential breakthroughs in precision gravity and providing a methodological foundation that could significantly enhance theoretical astrophysics's predictive capabilities.