Large deflection scattering, soft radiation and KMOC formalism

TL;DR

This paper extends the KMOC formalism to compute classical electromagnetic and gravitational memory effects from soft radiation, providing a non-perturbative approach applicable beyond large impact parameter scattering.

Contribution

It demonstrates that the KMOC formalism can be used to derive non-perturbative formulas for soft radiation memory effects in classical gauge theories and gravity.

Findings

Derived a non-perturbative formula for electromagnetic memory.

Connected the KMOC approach with classical soft theorems.

Validated results with previous classical soft theorem analyses.

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 cannot 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 and gravitational 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 the memory in the classical limit. We argue that the result obtained for electromagnetic memory, 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.