nucleon is empirically rather small [@tiator94]. Nevertheless the amplitude of $\eta N$ $s$-wave scattering is not as small as that for $\pi N$ scattering because of the contribution of the $s$-wave resonance $S_{11}(1535)$ which is actually a chiral partner of the nucleon — the lowest lying baryon with the opposite parity to the nucleon. This resonance has the mass slightly above the $\eta N$ threshold, $m_\eta+m_N = 1486$ MeV, and owing to its very strong coupling to the $\eta N$ channel \[with the branching ratio ${\rm Br}\;(S_{11}(1535)\to\eta N) \simeq 55\%$\] strongly enhances all interactions in this channel. A nice illustration of this feature is provided by Mainz data [@mcnicoll10] on the total cross section of $\eta$ photoproduction off protons. A huge near-threshold enhancement shown in Fig. \[eta-x-sect\] is just a manifestation of the $S_{11}(1535)$ resonance excited in the reaction $\gamma p\to
S_{11}(1535)\to\eta p$.

The $S_{11}(1535)$ resonance strongly contributes to the low-energy $\eta N$ scattering and, in particular, makes the threshold value of the $\eta N$ scattering amplitude (i.e. the $\eta N$ scattering length $a_{\eta N}$) positive. In the framework of a dynamical resonance model for the coupled channels $\pi N$, $\eta N$ and $\pi\pi
N$, Bhalerao and Liu [@bhalerao85] found 