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$Ξ$ baryon strong decays in a chiral quark model

The strong decays of $Ξ$ 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) $Ξ(1690)$ and $Ξ(1820)$ 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) $Ξ(1950)$ might correspond to several different $Ξ$ resonances. The broad states ($Γ\sim 100$ MeV) observed in the $Ξπ$ channel could be classified as the pure $J^P=5/2^-$ octet state $Ξ^0|70,^{4}8,1,1,5/2^->$ or the mixed state $|Ξ1/2^->_3 $ with $J^P=1/2^-$. The $Ξ$ resonances with moderate width ($Γ\sim 60$ MeV) observed in the $Ξπ$ 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 $|Ξ1/2^->_1$ might be candidates for the narrow width state observed in the $Λ\bar{K}$ channel, however, their spin-parity numbers are incompatible with the moment analysis of the data. (iii) $Ξ(2030)$ 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 $Ξ$ resonances, the observations in the $Ξ(1530)π$ and $Σ(1385) \bar{K}$ channels are necessary.