Magnetic corrections to the classical soft photon theorems at all orders

TL;DR

This paper extends classical soft photon theorems to include all subleading electric and magnetic corrections in dyonic scattering, providing explicit recursive formulas and demonstrating duality covariance.

Contribution

It introduces a comprehensive framework for classical soft expansions that incorporate magnetic charges and duality, expanding the scope of soft theorem analyses.

Findings

Explicit recursive formulas for electric and magnetic waveforms.

Manifest covariance of soft expansion under electric-magnetic duality.

Resummed waveforms for two-body scattering in time and frequency domains.

Abstract

When a set of charged or dyonic objects scatter and subsequently disperse, the process generically emits electromagnetic radiation. The classical soft photon theorem constrains the constant term and leading power-law fall-off of the emitted waveform at asymptotic times solely in terms of the momenta and charges of the incoming and outgoing particles. In this work, we extend the analysis to include the full tower of subleading corrections in the late-time and early-time expansion of the electric and magnetic waveforms, providing explicit expressions that depend only on the kinematic data and the electric and magnetic charges of the scattered objects. Using independent electric and magnetic potentials, we compute the full classical soft expansion for general dyonic scattering. We provide explicit, recursive expressions for the trajectory coefficients and the resulting electric and magnetic waveforms. The resulting soft expansion exhibits manifest covariance under the electric-magnetic duality. The electric and magnetic waveforms transform as an $SO(2)$ doublet under electric-magnetic duality. This provides a non-trivial consistency check on our formulation. For the specific case of two-body scattering, we obtain resummed expressions for the waveforms in both the time and frequency domains.