Radiated momentum in the Post-Minkowskian worldline approach via reverse unitarity

TL;DR

This paper calculates the momentum radiated during two-body scattering in general relativity using a novel worldline and reverse unitarity approach, providing an alternative to amplitude-based methods.

Contribution

It introduces a new method combining EFT worldline techniques with reverse unitarity to compute radiated momentum in the post-Minkowskian regime.

Findings

The emitted momentum matches previous results from other methods.

The approach avoids taking the classical limit of scattering amplitudes.

It demonstrates the effectiveness of particle physics techniques in gravitational radiation calculations.

Abstract

We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following \cite{Mougiakakos:2021ckm}, we derive the conserved stress-energy tensor linearly coupled to gravity generated by localized sources, at leading and next-to-leading order in $G$, and from that the classical probability amplitude of graviton emission. The total emitted momentum is obtained by phase-space integration of the graviton momentum weighted by the modulo squared of the radiation amplitude. We recast this as a two-loop integral that we solve using techniques borrowed from particle physics, such as reverse unitarity, reduction to master integrals by integration-by-parts identities and canonical differential equations. The emitted momentum agrees with recent results obtained by other methods. Our approach provides an alternative way of directly computing radiated observables in the post-Minkowskian expansion without going through the classical limit of scattering amplitudes.