Overlapping Resonances in Three-Particle Final States

Abstract

We investigate the properties of a three-particle final state within the context of the Lee model in order to determine if the overlap of two two-particle resonances might simulate a genuine three-particle resonance. The process $\theta +V\to \theta +\theta +N$ is examined. Matters have been so arranged that there is an $N\theta$ resonance called $V^{*}$. This can be brought about by introducing two elementary $V$ fields. The $V\theta$ sector remains exactly solvable and the method of solution is presented together with analytic expressions for the $N\theta$ scattering amplitude and the $V\theta$ elastic and production amplitudes. An analysis of the overlapping $V^{*}$ resonances in the final $N\theta \theta$ state shows that there is no effect not explicable in terms of two-particle phase space and simple one-particle-exchange dynamics. However, through a faulty selection of production events and a corresponding misapplication of unstable-particle theory, an apparent $V^{*}\theta$ resonance can be generated.