Subleading soft radiation during scattering of dressed states in QED

TL;DR

This paper demonstrates that properly corrected dressed states in QED suppress additional soft photon emission and render scattering amplitudes infrared-finite, establishing an effective infrared cutoff at a characteristic energy scale.

Contribution

It explicitly shows that subleading corrections to dressing functions eliminate soft photon emission and regulate infrared divergences in QED scattering amplitudes.

Findings

Soft photon emission is suppressed with corrected dressings.

Infrared divergences are canceled at the energy scale $E_d$.

An infrared finite S-matrix can be formulated.

Abstract

We study soft photon emission during scattering of Faddeev-Kulish charged states in QED, at leading order in perturbation theory. The charged asymptotic particles are accompanied by clouds of an infinite number of soft photons of energy less than a characteristic infrared scale $E_d$. When the corresponding ``dressing'' functions are suitably corrected to subleading order in the soft momentum expansion, as advocated in recent work by Choi and Akhoury, we show explicitly that the emission of additional radiative soft photons with energy less than $E_d$ is completely suppressed. Moreover, the dressing renders the elastic amplitudes infrared-finite, order by order in perturbation theory, regulating the infrared divergences due to virtual soft photons, at the energy scale $E_d$. Therefore, the characteristic energy scale of the soft photons in the clouds provides an effective infrared cutoff, allowing for the formulation of an infrared finite S-matrix.