Khuri-Treiman-Type Equations for Three-Body Decay and Production Processes

Abstract

We discuss some aspects of a model for three-body decay (or production) processes based essentially on the elastic approximation in each subenergy channel. A simple method is given to reduce the dispersion integral equations into a single-variable form. In passing, some properties of the triangle-graph amplitude with respect to an internal mass are clarified. Finally we discuss the conditions under which the model can nearly satisfy three-body unitarity; in particular, it is shown that, by simulating high-energy effects in each subenergy variable by a convenient cutoff procedure, we can satisfy three-body unitarity, at least in the decay (or production) region. We restrict ourselves in this paper to the lowest possible angular momentum states.