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 $\rho K$.

• Received 4 August 1978

DOI:https://doi.org/10.1103/PhysRevD.19.239