Large deflection scattering, soft radiation and KMOC formalism

TL;DR

The paper addresses computing electromagnetic memory in four dimensions within the KMOC framework beyond the traditional large impact parameter regime. It demonstrates that soft-factorization and inclusive observables in KMOC can reproduce the classical memory via a saddle-point analysis of soft photon emission, aligning with Laddha's classical-soft theorem results. The key contribution is a nonperturbative formula for electromagnetic memory in the classical limit, where the soft flux is determined by the leading soft factor $S^{(0)}$ and the semi-inclusive cross section. This work builds a bridge between on-shell amplitude methods and classical memory phenomena, with potential extensions to gravitational memory and more general radiative processes.

Abstract

KMOC (Kosower, Maybee, and O'Connell) formalism is an approach to analyze classical scattering in gauge theories and gravity using a class of ``inclusive'' observables which can be computed solely from on-shell amplitudes \cite{Kosower:2018adc}. This formalism has led to striking developments in the context of perturbative scattering, which corresponds to large impact parameter scattering. As a result, in its current form, the KMOC formulae can not be directly applied to processes for generic values of the impact parameter. However, there is a domain where the relationship between classical radiation and on-shell amplitudes can be stretched beyond large impact parameter scattering. This regime is defined by the soft expansion of outgoing radiation. It is thus natural to ask if such soft radiative fields can be computed using the basic paradigm set by the KMOC formalism. In this short note, we show that this is indeed the case for electromagnetic memory. That is, we compute an inclusive observable associated with soft flux at ${\cal I}^{+}$ and show that, irrespective of the details of the hard scattering, this observable defines a non-perturbative formula for electromagnetic memory in the classical limit. We argue that the result obtained using the KMOC paradigm is consistent with those in \cite{Laddha:2018rle}, where the classical limit of the quantum soft theorem was taken using saddle point analysis.