TL;DR
This paper provides a comprehensive pedagogical overview of coupled-channel scattering methods in hadronic physics, emphasizing theoretical frameworks, practical parameterizations, and applications to resonance phenomena, with relevance to related physical systems.
Contribution
It introduces a unified approach to coupled-channel scattering, combining various techniques like the $N/D$ method, Lippmann-Schwinger equation, and Riemann sheet analysis, enhancing understanding and application in hadronic and related physics.
Findings
Develops a parameterization for partial wave amplitudes that respects unitarity and analyticity.
Explores the role of Riemann sheets in understanding resonance behavior.
Addresses scattering near threshold with practical applications to nuclear and atomic physics.
Abstract
This article provides a pedagogical exploration of coupled-channel scattering in hadronic physics, focusing on theoretical methodologies, and practical applications. It covers key concepts such as the method, Castillejo-Dalitz-Dyson poles, and the generalization of these techniques to coupled channels. The article also presents a parameterization for partial wave amplitudes, ensuring unitarity and analyticity, and addresses scattering near the threshold of dominant channels, with use also of the Lippmann-Schwinger equation. Additionally, it explores final-state interactions, Omn\`es and Muskhelishvily solutions, the Khuri-Treiman approach, and the two-potential model for resonant event distributions, highlighting the role of Riemann sheets in resonance behavior. These methods are also applicable to related fields like nuclear and atomic physics.
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Taxonomy
TopicsRadiation Effects in Electronics