S-Wave Pseudoscalar-Meson-Baryon Scattering in a Simple Model with BrokenSU(3)Symmetry

A model of $S$-wave pseudoscalar-meson-baryon scattering is studied in which the force is due to vectormeson exchange. The potential is approximated by a static Yukawa potential and the kinematics is simplified. The actual physical masses of the particles are used so that $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry is broken. The resulting problem reduces to a set of coupled-channel Schrödinger equations which are solved exactly on a computer. The $K$ matrix and the eigenphases are calculated. Several examples of virtual bound-state resonances are found. The model yields a ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$ as a virtual bound state of $\overline{K}N$ and an ${N_{\frac{1}{2}}}^{*}\mathrm{}\left(1570\right)\mathrm{}$ as a virtual bound state of $K\Sigma$.