The pseudoscalar meson and baryon octet interaction with strangeness zero in the unitary coupled-channel approximation

The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation, In addition to the Weinberg-Tomozawa term, the contribution of the $s-$ and $u-$ channel potentials in the S-wave approximation are taken into account. In the sector of isospin $I=1/2$ and strangeness $S=0$, a pole is detected in the reasonable region on the complex energy plane of $\sqrt{s}$ in the center of mass frame by analyzing the behavior of the scattering amplitude, which is higher than the $\eta N$ threshold and lies on the third Riemann sheet. Thus it can be regarded as a resonance state and might correspond to the $N(1535)$ particle in the review of the Particle Data Group(PDG). The coupling constants of this resonance state to the $\pi N$, $\eta N$, $K \Lambda$ and $K \Sigma$ channels are calculated, and it is found that this resonance state couples strongly to the hidden strange channels. Apparently, the hidden strange channels play an important role in the generation of the resonance state with strangeness zero. The interaction of the pseudoscalar meson and the baryon octet is repulsive in the sector of isospin $I=3/2$ and strangeness $S=0$, therefore, no resonance state can be generated dynamically.