Coupled channels approach to $\eta N$ and $\eta' N$ interactions

Abstract

We present a coupled channels separable potential approach to $\eta N$ and $\eta'N$ interactions using a chiral-symmetric interaction kernel. The s-wave $\pi N$ amplitudes and $\pi^{-}p$ induced total cross sections are reproduced satisfactorily in a broad interval of energies despite limiting the channel space to two-body interactions of pseudoscalar mesons with the baryon ground-state octet. It is demonstrated that an explicit inclusion of the $\eta_0$ meson singlet field leads to a more attractive $\eta N$ interaction, with the real part of the scattering length exceeding 1 fm. The $\eta'N$ diagonal coupling appears sufficient to generate an $\eta'N$ bound state but the inter-channel dynamics moves the respective pole far from physical region making the $\eta'N$ interaction repulsive at energies around the channel threshold. The $N^{*}(1535)$ and $N^{*}(1650)$ resonances are generated dynamically and the origin and properties of the $S$-matrix poles assigned to them are studied in detail. We also hint at a chance that the $N^{*}(1895)$ state might also be formed provided a suitably varied model setting is found.