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$Θ^+$ baryon, $N^* (1685)$ resonance, and $πN$ sigma term in the context of the LEPS and DIANA experiments

We reexamine properties of the baryon antidecuplet $Θ^+$ and $N^*$, and the $πN$ sigma term within the framework of a chiral soliton model, focusing on their dependence on the $Θ^+$ mass. It turns out that the measured value of the $N^*$ mass, $M_{N^*}=1686$ MeV, is consistent with that of the $Θ^+$ mass $M_{Θ^+}=1524$ MeV by the LEPS collaboration. The $N^*\to Nγ$ magnetic transition moments are almost independent of the $Θ^+$ mass. The ratio of the radiative decay width $Γ_{nn^*}$ to $Γ_{pp^*}$ turns out to be around 5. The decay width for $Θ^+\to NK$ is studied in the context of the LEPS and DIANA experiments. When the LEPS value of the $Θ^+$ mass is employed, we obtain $Γ_{ΘNK} =(0.5\pm0.1)$ MeV. The $πN$ sigma term is found to be almost independent of the $Θ^+$ mass. In addition, we derive a new expression for the $πN$ sigma term in terms of the isospin mass splittings of the hyperon octet as well as that of the antidecuplet $N^*$.