$\Xi$ 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.

14 pages, 7 figures

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