Relativistic Three-Pion Calculation. III

Abstract

A model for three-spinless-meson relativistic resonances, based on the Alessandrini-Omnes generalization of the Faddeev equations, which was explained in two previous papers, is studied in all three-pion states with angular momentum $J<3$. The only part of the two-body amplitude which is taken into account is the $\ensuremath{\rho}$ resonance. The separation of isospin is shown explicitly, and it is explained how the momentum-space equations reduce to only one when Bose statistics is taken into account. The results do not suggest the dynamical origin of the ${A}_{2}$, and many isoscalar resonances are found in a small energy region.