Analysis of 3-Body Angular Momentum States inπN→ππN

A relativistic formalism for analyzing 3-body angular momentum states in production processes is presented in detail together with examples of several processes $\pi N\to \pi \pi N$ at different energies below 1 BeV. In the final state we assume either one or several 3-particle angular momentum states, belonging to only one complete set of states. This enables us to distinguish clearly between different partial-wave transitions, and to make our analysis in a systematic way. As a dynamical assumption we use the isobar model, and allow only a minimum number of transitions in order to minimize the number of free parameters. Our formulas are written in terms of variables used in the Faddeev theory with separable approximation; thus they can be applied for testing solutions of the Faddeev equation.