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arXiv · 2407.15382

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

J. A. Oller·Marcela Peláez
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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.

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J. A. Oller, Marcela Peláez. 2024-07-22. Unitarization of electron scattering with an external potential at NLO in QED. https://arxiv.org/abs/2407.15382

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