Radiation Reaction from Soft Theorems

TL;DR

This work reveals a direct link between radiation-reaction (RR) effects at 3PM order in gravitational scattering and soft (bremsstrahlung) theorems by showing that the RR component of the eikonal is determined by the IR-divergent part of the two-loop imaginary component via $\lim_{\epsilon\to0}{\rm Re}\,2\delta_2^{(rr)} = -\lim_{\epsilon\to0}[\pi \epsilon \,{\rm Im}\,2\delta_2]$, which in turn relates to the zero-frequency limit of the radiated energy $\frac{dE^{rad}}{d\omega}(\omega\to0)$. Employing unitarity and analyticity, the authors compute the IR-divergent piece of ${\rm Im}\,2\delta_2$ by sewing leading soft $2\to3$ amplitudes and show that, after summing over massless states, the resulting expressions reproduce Damour’s GR 3PM results and extend naturally to Jordan-Brans-Dicke theory. The analysis, first demonstrated in ${\cal N}=8$ supergravity and then carried over to GR and JB-D, provides a simpler route to RR terms at the 3PM level and suggests a broad applicability of the soft-theorem perspective in classical gravitational scattering.

Abstract

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.