Chiral unitary approach to hadron spectroscopy

Abstract

The s-wave meson-baryon interaction in the $S = -1$, $S= 0$ and $S= -2$ sectors is studied by means of coupled channels, using the lowest-order chiral Lagrangian and the N/D method or equivalently the Bethe-Salpeter equation to implement unitarity. This chiral approach leads to the dynamical generation of the $\Lambda (1405)$, $\Lambda(1670)$ and $\Sigma(1620)$ states for $S = -1$, the $N^*(1535)$ for $S= 0$ and the $\Xi(1620)$ for $S= -2$. We look for poles in the complex plane and extract the couplings of the resonances to the different final states. This allows identifying the $\Lambda (1405)$ and the $\Lambda(1670)$ resonances with $\bar{K}N$ and $K\Xi$ quasibound states, respectively. Our results are found to be incompatible with the measured properties of the $\Xi(1690)$ resonance, thus ruling this state out as the remaining member of this octet of dynamically generated resonances. We therefore assign $1/2^-$ for the spin and parity of the $\Xi(1620)$ resonance as the $S=-2$ member of the lowest-lying $1/2^-$ octet.