RELATION BETWEEN SCATTERING AND PRODUCTION AMPLITUDES - CONCERNING A PARTICLE IN PI-PI SYSTEM

In a series of previous papers the present authors and collaborators h ave shown strong evidence for existence of the long-sought sigma parti cle by analyzing the pi pi-scattering and pi pi-production processes, applying, respectively, the IA method and the VMW method. In this pape r we examine the relation between the scattering amplitude T and the p roduction amplitude F from the viewpoint of unitarity and the final st ate interaction (FSI) theorem by using a simple field theoretical mode l. As a result it is shown that the amplitudes in the physical state r epresentation are directly represented through the Breit-Wigner amplit udes of the relevant resonances, and the respective forms of Y and F c oincide with those in the IA and VMW methods, justifying our methods o f ana;lyses.