Gravitational radiation from inspiralling compact binaries to N$^3$LO in the Effective Field Theory approach

TL;DR

This paper advances the theoretical understanding of gravitational waves from inspiralling binaries by computing the N$^3$LO Hamiltonian and flux using EFT, confirming 3PN flux results and setting the stage for future spin and higher-order analyses.

Contribution

It provides the first ambiguity-free N$^3$LO gravitational-wave flux calculation for inspiralling binaries within the EFT framework.

Findings

Confirmed the 3PN gravitational-wave flux for quasi-circular orbits.

Performed two-loop Feynman integral calculations within dimensional regularization.

Established a foundation for including spin effects and higher-order terms.

Abstract

Within the context of the Effective Field Theory (EFT) framework to gravitational dynamics, we compute the Hamiltonian, source quadrupole moment, and gravitational-wave energy flux for (non-spinning) inspiralling compact binaries at next-to-next-to-next-to leading order (N$^3$LO) in the Post-Newtonian (PN) expansion. We use the recently developed $d$-dimensional multipole-expanded effective theory, and explicitly perform the matching to the (pseudo-) stress-energy tensor. The calculation involves Feynman integrals up to three- (conservative) and two-loop (radiative) orders, evaluated within dimensional regularization. Our (ambiguity-free) results confirm (for the first time) the value of the gravitational-wave flux for quasi-circular orbits at 3PN order, while paving the way forward to the inclusion of spin effects as well as higher order computations.