Unstable-particle scattering and an analytic quasi-unitary isobar model

An explicit model is constructed for the scattering of unstable particles such as $\rho \pi \to \rho \pi$, $K^{*}\pi \to K^{*}\pi$, and $\rho K\to \rho K$. It has correct analyticity properties and satisfies quasi-two-body unitarity. The essential ingredient of the approach is a Chew-Mandelstam function for unstable particles in which the particle-resonance branch cuts are located in second Riemann sheets of the three-particle complex energy plane. The model shall be applied in future studies of final states such as $\rho \pi$, $K^{*}\pi$, and $\rho K$.