Analyzing $\Xi (1620)$ in the molecule picture in the Bethe-Salpeter equation approach

Abstract

In this work, we assume that the observed state $\Xi (1620)$ is a $s$-wave $\Lambda \bar{K}$ or $\Sigma \bar{K}$ bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for $\Xi (1620)$ in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the $\Lambda \bar{K}$ and $\Sigma \bar{K}$ systems numerically and find that the $\Xi (1620)$ can be explained as $\Lambda \bar{K}$ and $\Sigma \bar{K}$ bound states with $J^P=1/2^{-}$, respectively. Then we calculate the decay widths of $\Xi (1620)\to \Xi \pi$ in these two different molecule pictures systems, respectively.

arXiv commentarXiv admin note: text overlap with arXiv:1710.07424

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Cited by in corpus (6)

• Accessing the strong interaction between $\Lambda$ baryons and charged kaons with the femtoscopy technique at the LHC
• $\bar{K}\Lambda$ molecular explanation to the newly observed $\Xi (1620{)}^0$
• Study on possible molecular states composed of ${\Lambda }_c\bar{D}$ (${\Lambda }_{b}B$) and ${\Sigma }_c\bar{D}$ (${\Sigma }_{b}B$) within the Bethe-Salpeter framework
• Study ${\Xi }_c^{+}\to \Lambda {\bar{K}}^0{\pi }^{+}$ and search for the low-lying baryons $\Xi (1/2^{-})$ and $\Sigma (1/2^{-})$
• Structure of the $\mathbf{\Lambda }(1670)$ resonance
• The pseudoscalar meson and baryon octet interaction with strangeness $S=-2$ in the unitary coupled-channel approximation