Unitarization of electron scattering with an external potential at NLO in QED
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| Format: | Preprint |
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2024
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| _version_ | 1866916480367460352 |
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| author | Oller, J. A. Peláez, Marcela |
| author_facet | Oller, J. A. Peláez, Marcela |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_15382 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarization of electron scattering with an external potential at NLO in QED Oller, J. A. Peláez, Marcela High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Unitarization of electron scattering with an external potential at NLO in QED |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.15382 |