Relativistic Three-Pion Calculation. II

Abstract

The calculation of the $I=0\mathrm{}$, $J^P=1^{-}$ three-pion state is done on the basis of previously derived equations. The two-body amplitude is assumed to be well represented by the pole of the $\rho$. Particular choices for the resonance form factors appearing in the equations are discussed. The behavior of the eigenvalues of the Faddeev kernel is exhibited, and it is explained why the $\omega$ meson does not appear in such a model. A resonance is found at relatively high energy which does not depend on the choice of the form factors. This resonance seems to correspond to the experimental $E$ meson.