Unitarization of electron scattering with an external potential at NLO in QED

TL;DR

This paper develops a method to compute infrared-finite, unitarized electron scattering amplitudes in QED with an external Coulomb potential at NLO, enabling analysis of bound states and nonperturbative effects.

Contribution

It introduces a novel approach combining infrared divergence removal with unitarization techniques for electron scattering in QED, applicable to various systems.

Findings

Infrared-finite one-loop partial-wave amplitudes derived

Unitarization methods applied to analyze bound states

Identification of the fundamental bound state in S wave

Abstract

We have calculated the one-loop scattering amplitude of an electron by an external Coulomb potential in QED free of infrared divergences. This feature is achieved by applying the Faddeev-Kulish formalism, which implies a redefinition of both the asymptotic electronic states and of the $S$ matrix. Additionally, we have also derived the infrared-finite one-loop partial-wave amplitudes for this process by applying a recent method in the literature. Next, these partial-wave amplitudes are unitarized based on analyticity and unitarity by employing three different methods of unitarization: the algebraic $N/D$ method, the Inverse Amplitude Method and the first iterated $N/D$ method. Then, we have studied several partial waves both for physical momentum and for complex ones to look for bound-state poles. The binding momentum for the fundamental bound state in $S$ wave is discussed with special detail. This is a wide-ranging method for calculating nonperturbative partial-wave amplitudes for infinite-range interactions that could be applied to many other systems.