Title:
“The strawberry grows underneath the nettle”: Computing radiated angular momentum at (3PM) and (e^6) from the impact parameter.

Abstract:
Analytic results for radiative fluxes are of interest for gravitational-wave modelling, as they can be used to inform the Effective-One-Body (EOB) formalism. While radiated energy has been computed to (5PM 1SF), results for radiated angular momentum are lagging behind: It is not known beyond (3PM). To pave the way for radiated angular momentum (ΔL) at (4PM), we propose a novel method to calculate this observable within the WQFT framework. The central quantity is the change in the impact parameter. While its conservative part is badly behaved and both UV and IR divergent, its dissipative part is finite and contains the information needed to derive ΔL. We may split all contributions into two categories, depending on the scaling of the loop momenta with the energy of the outgoing worldline. Its “dynamical” part can be computed in analogy to the impulse. The “static” contributions, related to the wave memory, are accessible through certain n-point functions, which we named “static correlators”. This method is designed to be applicable at general PM orders. We have demonstrated its functionality by reproducing from it the known result of the 3PM radiated angular momentum, as well as deriving the equivalent result in electrodynamics, which was not covered in the literature so far.