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

Abstract

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