Analytic Structure of Partial-Wave Amplitudes for Production and Decay Processes

We consider a model theory for studying overlapping final-state interaction effects in 3-body production and decay amplitudes. The model is given in terms of dispersion relations similar to those given by Khuri and Treiman for the process $K\to 3\pi$. We extend the partial-wave projections into the complex plane, and determine their analytic properties, giving explicitly a set of cuts and discontinuities. These consist of the usual right-hand cut with normal discontinuity, together with a "left-hand" cut for which the discontinuity is expressed as an integral over the projections. The right-hand cut can be factored out in the usual way, and thus one can hope to obtain the solution by iteration for the left-hand cut contribution.