Investigation of Resonances in the $\Sigma ({1/2}^{-})$ System Based on the Chiral Quark Model

Abstract

In this work, we investigate the resonance structures in the $\Sigma (1/2^{-})$ system from both three-quark and five-quark perspectives within the framework of the chiral quark model. An accurate few-body computational approach, the Gaussian Expansion Method, is employed to construct the orbital wave functions of multiquark states. To reduce the model dependence on parameters, we fit two sets of parameters to check the stability of the results. The calculations show that our results remain stable despite changes in the parameters. In the three-quark calculations, two $\Sigma (1/2^{-})$ states are obtained with energies around 1.8~GeV, which are good candidates for the experimentally observed $\Sigma (1750)$ and $\Sigma (1900)$. In the five-quark configuration, several stable resonance states are identified, including $\Sigma \pi$, $N\bar{K}$, and $N{\bar{K}}^{\ast }$. These resonance states survive the channel-coupling calculations under the complex-scaling framework and manifest as stable structures. Our results support the existence of a two-pole structure for the $\Sigma (1/2^{-})$ system, predominantly composed of $\Sigma \pi$ and $N\bar{K}$ configurations, analogous to the well-known $\Lambda (1380)$-$\Lambda (1405)$ ($\Sigma \pi$-$N\bar{K}$) system. On the other hand, although the energy of the $N{\bar{K}}^{\ast }$ configuration is close to that of $\Sigma (1750)$ and $\Sigma (1900)$, the obtained width is not consistent with the experimental values. This suggests that the $N{\bar{K}}^{\ast }$ state needs to mix with three-quark components to better explain the experimental $\Sigma (1750)$ and $\Sigma (1900)$ states. According to our decay width calculations, the predicted two resonance states are primarily composed of $\Sigma \pi$ and $N\bar{K}$, with their main decay channel being $\Lambda \pi$.