Coupled-channel formalism

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 $N/D$ 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.