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

IF 5.4 1区物理与天体物理 Q1 Physics and Astronomy

Journal of High Energy Physics Pub Date : 2024-11-19 DOI:10.1007/JHEP11(2024)113

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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在 QED 的 NLO 阶段，电子散射与外部电势的统一化

我们计算了电子在 QED 中无红外发散的外部库仑势单环散射振幅。这一特征是通过应用法迪夫-库利什形式主义实现的，这意味着对渐近电子态和 S 矩阵的重新定义。此外，我们还运用文献中的一种最新方法，推导出了这一过程的红外无限单环偏波振幅。接下来，我们采用三种不同的单位化方法：代数 N/D 法、逆振幅法和第一次迭代 N/D 法，基于解析性和单位性对这些偏波振幅进行了单位化。然后，我们研究了几种物理动量和复动量的偏波，以寻找束缚态极点。我们特别详细地讨论了 S 波中基本束缚态的束缚动量。这是一种计算无穷程相互作用的非微扰偏波振幅的广泛方法，可应用于许多其他系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of High Energy Physics 物理-物理：粒子与场物理

CiteScore

10.30

自引率

46.30%

发文量

2107

审稿时长

1.5 months

期刊介绍： The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).