Singularities in the Unphysical Sheets and the Isobar Model

Abstract

Scattering amplitudes involving two- and three-particle states are continued across the inelastic section of the unitarity cut, and the singularities in the unphysical sheets thus reached are determined. Associated with an unstable particle is a complex unitarity cut, through which we further continue into another unphysical sheet. Dynamical singularities associated with a Born-type diagram for the three-particle scattering amplitude are found to be present in the elastic scattering and the production amplitudes also because of the coupling by unitarity. These singularities are isolated from the physical region by the complex unitarity cut and thus cannot be directly responsible for any resonance phenomenon. However, if the interaction force is favorable, a resonance pole can occur in a different Riemann sheet in the vicinity of these singularities. This resonance pole is directly accessible from the physical region and can therefore give rise to a resonance.