Over its two-year implementation period, the GWtheory project successfully executed its research plan and achieved all core scientific objectives, while strategically refining secondary priorities to align with the most impactful emerging directions in gravitational-wave physics.
Within the effective field theory (EFT) framework, computing physical observables such as the momentum impulse and scattering angle ultimately reduces to evaluating a specific class of Feynman integrals. For two-body dynamics, these integrals depend on a single dimensionless parameter—the scalar product of the initial velocities of the two bodies, denoted y. Separating the full scattering quantities into local-in-time and nonlocal-in-time contributions, however, introduces integrals containing logarithmic terms that depend on both y and the mass ratio. In particular, for integrals arising from local-in-time effects, we employ a power expansion in the mass ratio (also known as the self-force expansion). This expansion converts logarithmic terms into rational functions, which are significantly easier to manipulate, but at the cost of increasing the powers of propagators and numerators as higher orders are pursued. The GWtheory project developed novel, optimized integration-by-parts (IBP) reduction techniques tailored to these integrals, and established efficient methods for solving the elliptic differential equations satisfied by the master integrals. Using these newly developed tools, we successfully performed analytic calculations of the 5PM local-in-time conservative dynamics at first order in the mass-ratio expansion (1SF), and subsequently extended the precision to the tenth order (10SF). This achievement represents a major advance in the field, as it removes a critical barrier to the analytic continuation between scattering and bound-state dynamics.
In response to the rapid conceptual evolution of gravitational-wave physics, the project strategically refined its research plan to encompass alternative gravity paradigms, thereby maximizing its long-term scientific impact. This strategic adjustment led to the systematic generalization of the worldline effective field theory framework to study compact binaries in theories beyond general relativity. The framework was specifically applied to scalar-tensor and Einstein-scalar-Gauss-Bonnet (ESGB) gravity—two particularly well-motivated and phenomenologically rich alternative theories. For both theories, we derived analytic expressions for the momentum impulse and scattering angle up to 3PM order.
