$Ξ$ baryon strong decays in a chiral quark model

Abstract: The strong decays of $\Xi$ baryons up to N=2 shell were studied in a chiral quark model. The strong decay properties of these well-established ground decuplet baryons were reasonably described. We found that (i) $\Xi(1690)$ and $\Xi(1820)$ could be assigned to the spin-parity $J^P=1/2^-$ state $|70,^{2}{8},1,1,1/2^->$ and the spin-parity $J^P=3/2^-$ state $|70,^{2}{8},1,1,3/2^->$, respectively. Slight configuration mixing might exist in these two negative parity states. (ii) $\Xi(1950)$ might correspond to several different $\Xi$ resonances. The broad states ($\Gamma\sim 100$ MeV) observed in the $\Xi\pi$ channel could be classified as the pure $J^P=5/2^-$ octet state $\Xi^0|70,^{4}8,1,1,5/2^->$ or the mixed state $|\Xi 1/2^->_3 $ with $J^P=1/2^-$. The $\Xi$ resonances with moderate width ($\Gamma\sim 60$ MeV) observed in the $\Xi\pi$ channel might correspond to the $J^P=1/2^+$ excitation $|56,^{4}10,2,2,1/2^+>$. The second orbital excitation $|56,^{4}10,2,2,3/2^+>$ and the mixed state $|\Xi 1/2^->_1$ might be candidates for the narrow width state observed in the $\Lambda \bar{K}$ channel, however, their spin-parity numbers are incompatible with the moment analysis of the data. (iii) $\Xi(2030)$ could not be assigned to either any spin-parity $J^P=7/2^+$ states or any pure $J^P=5/2^+$ configurations. It seems to favor the $|70,^{2}8,2,2,3/2^+>$ assignment, however, its spin conflicts with the moment analysis of the data. To find more $\Xi$ resonances, the observations in the $\Xi(1530)\pi$ and $\Sigma(1385) \bar{K}$ channels are necessary.