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 $J<\mathrm{}3\mathrm{}$. The only part of the two-body amplitude which is taken into account is the $\rho$ 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.