Relativistic partial-wave analysis for three-meson systems. II

Abstract

We extend our relativistic partial-wave analysis to the $Ig0$ channels of the three-pion system. For the sake of definiteness, we apply our general procedure to the minimal-dynamics $K$-matrix model. In particular, we first generate properly symmetrized three-pion states using a group-theoretical approach. Using these, we then construct symmetrized scattering amplitudes and develop the minimal-dynamics $K$-matrix equations satisfied by the operators which enter into the symmetrized amplitudes. We find that for the $I=1$ channel of the threepion system, the ${i}_{\mathrm{ij}}=0,2$ subsystem isospin channels contribute to the scattering amplitude on the same footing as does the ${i}_{\mathrm{ij}}=1$ subsystem isospin channel. Thus the calculated properties of $I=1$ three-pion resonances may be as dependent on the ${i}_{\mathrm{ij}}=0$ phase parameters as on the ${i}_{\mathrm{ij}}=1$ phase parameters which were assumed to be dominant in a number of previous calculations.