Exotic decay modes of the nucleon resonance $N^*(1535)$ and the $θ^+$ problem

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Baryon resonance state with strangeness $S = +1$ observed in systems $p K^0$ and $n K^+$ is interpreted as a result of the decay $N^{*+} \to p η$ of the well-known resonance $N^*(1535)$ (with spin-parity $j^P = {1/2}^-$ and mass $m \approx 1.54$ GeV) and the subsequent oscillation $η\rightleftarrows K^0$. It is argued that the latter is noticeably enhanced by the neighbourhood of the $η$ and $K^0$ levels and the gluon exchanges of the "penguin" form.
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