Signature of $N^{\star}$ resonance in mass spectrum of the $K\bar{K}N$ decay channels

Abstract

Three-body calculations of $I=\frac{1}{2}$, $J^{\pi}=\frac{1}{2}^{+}$ state of $K\bar{K}N$ system were performed. Using separable potentials for two-body interactions in the Faddeev equation, different reaction process for $K\bar{K}N$ three-body system were studied. Within this method, the $\pi\Sigma{K}$ and $\pi\eta{N}$ mass spectra were extracted. Different types of $\bar{K}N-\pi\Sigma$ potentials based on phenomenological and chiral SU(3) approach were used and the dependence of the mass spectra to the $\bar{K}N$ model of interaction were studied. It was shown that the $\pi\Sigma{K}$ and $\pi\eta{N}$ mass spectra could be a useful tool to study the properties of the $N^{\star}$ resonance.