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

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.