Section 50 in the PDG (Particle Data Group Collaboration et al., 2024) provides an overview of scattering theory and resonance parametrizations. Aitchison (1972) first introduced the \(K\)-matrix formalism and Chung & Klempt (1995), Chung et al. (1995), Bargiotti et al. (2002), and Peters (2006) provide a comprehensive review of the formalism.
The Chew–Mandelstam function for \(S\) waves is described in Basdevant & Berger (1977), Equation (3.8). It also discusses background unitarization, see Equation (3.5). A great introduction to unitarity, analyticity and crossing symmetry can be found by Aitchison (2015).
Some great examples of coupled analyses with the \(K\)-matrix formalism are Anisovich & Sarantsev (2003) and Albrecht et al. (2020).
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