Relativistic, final-state interactions and unitarity

Abstract : The residual interactions between hadrons is sufficiently strong to result in repeated, non-perturbative scattering between different final-states channels. At moderate CM energies ($1--3$~GeV), the inclusion of such final-state interactions is crucial, but requires solving coupled sets of relativistic, integral equations. Here, a relativistic, quantum mechanical framework is introduced and solved that includes interactions between one-, two- and three-body states. The framework is then used to study $\pi \pi$ from threshold to 1.5 GeV.