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

Understand

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.