On resonances in a system of coupled two-particle channels

Abstract

A simple model of a system of coupled two-particle channels is solved exactly. It is shown that a narrow resonance can occur at a relatively low energy, especially if all of the two-particle channels have angular momentum greater than zero, or if one nearby “closed” S-wave channel is present. The resonance manifests itself at a given energy in all of the T-matrix elements, although it may be considerably weaker in some elements than in others. Within the framework of the model, the essential dynamical origin of the resonance is the coupling between the channels, plus, in addition, an interaction peculiar to one of the channels. If the Born matrix elements coupling different channels have the property that they grow rapidly with increasing energy, this can result in a resonance behavior for the transition matrix at a lower energy where these Born elements are still small. An attempt is made to see whether this type of resonance might describe the isotopic spin zero, negative strangeness, meson-baryon resonances observed at 1405 Mev and at 1525 Mev. Both of these resonances satisfy a requirement of the model that the center-of-mass momenta in all of the coupled two-particle channels be relatively low. Within the framework of this model, the 1525 Mev resonance might be viewed as a “virtual-bound” state of the Λ hyperon and an isoscalar, scalar meson (or π−π resonant state) with total energy of about 400 Mev. The 1405 Mev resonance might similarly be viewed as a “virtual-bound” state of the Λ hyperon and an isoscalar, scalar system with total energy about twice the pion mass.