Gravitational radiation from inspiralling compact binaries to N3LO in the effective field theory approach

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 (nonspinning) inspiralling compact binaries at next-to-next-to-next-to leading order (N³LO) 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 quasicircular orbits at 3PN order, while paving the way forward to the inclusion of spin effects as well as higher-order computations.