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We investigate the strong and radiative decay widths of the narrow nucleonresonances $N^*(1685)$ and $N^{\ast}(1726)$ within the framework of the SU(3)chiral quark-soliton model. All the relevant parameters are taken from thoseused to describe the properties of the baryon octet and decuplet in previousworks. The masses of the antidecuplet nucleon and the eikosiheptaplet (27-plet)nucleon with spin 3/2 are determined respectively to be $(1690.2\pm 10.5)\,\mathrm{MeV}$ and $(1719.6\pm7.4)\,\mathrm{MeV}$. The decay width for$N^{\ast}(1685)\to \eta + N$ is found to be approximately three times largerthan that for $N^{\ast}(1685)\to \pi +N$. The width of the decay$N^{\ast}\left(1726\right)3/2^+\to \eta +N$ is even about 31 times larger thanthat of $N^{\ast}\left(1726\right)3/2^+\to \pi + N$. The ratio of the radiativedecays for $N^*(1685)$ is obtained to be$\Gamma_{nn^*(1685)}/\Gamma_{pp^*(1685)}=8.62\pm3.45$ which explains very wellthe neutron anomaly. In contrast, we find$\Gamma_{pp^*(1726)}/\Gamma_{nn^*(1726)}=3.72\pm0.64$, which indicates that theproduction of $N^*(1726)$ is more likely to be observed in the proton channel.We also examined the decay modes of these narrow nucleon resonances with thestrangeness hadrons involved.

New narrow nucleon resonances $N^{\ast}(1685)$ and $N^{\ast}(1726)$ within the chiral quark-soliton model