Internal structures of the baryons $Ξ(2030)$ and $Ξ(2120)$

Abstract: Currently, there is much controversy surrounding the interpretation of the $\Xi(2030)$ and $\Xi(2012)$ as traditional hadrons containing double strange quarks. In particular, the ratios of the partial decay widths into $\Lambda\bar{K}$ and $\Sigma\bar{K}$ for $\Xi(2030)$ cannot obtain a suitable explanation under the $qss$ three quark structure~\cite{Xiao:2013xi}. Thus, we suggest the $\Xi(2030)$ and $\Xi(2012)$ to be $VB(=\bar{K}^{}\Sigma/\rho\Xi/\bar{K}^{}\Lambda/\phi\Xi/\omega\Xi)$ molecular states. In this work, we perform a systematical investigation of possible molecular states from the $VB(=\bar{K}^{}\Sigma/\rho\Xi/\bar{K}^{}\Lambda/\phi\Xi/\omega\Xi)$ interaction. The interaction of the system considered is described by the $t$-channel vector ($\rho,\omega,\phi,\bar{K}^{*}$) and pseudoscalar ($\pi,\eta,\bar{K}$) mesons exchanges. By solving the non-relativistic Schr\"{o}dinger equation with the obtained one-boson-exchange potentials, the $VB(=\bar{K}^{}\Sigma/\rho\Xi/\bar{K}^{}\Lambda/\phi\Xi/\omega\Xi)$ bound states with different quantum numbers are searched. The calculation suggests that $\Xi(2030)$ can be assigned as a $P$-wave $\bar{K}^{}\Sigma/\rho\Xi/\bar{K}^{}\Lambda/\phi\Xi/\omega\Xi$ molecular state with spin parity $J^P=5/2^{+}$. The calculation also predict the existence of four $\bar{K}^{}\Sigma/\rho\Xi/\bar{K}^{}\Lambda/\phi\Xi/\omega\Xi$ bound states with $J^P=1/2^{\pm}$ and $J^P=3/2^{\pm}$. The $\Xi(2012)$ may be a candidate for one of these four bound states. If $\Xi(2012)$ is an $S$-wave molecular state with $J^P=1/2^{-}$ or $J^P=3/2^{-}$, we suggest determining its spin and parity by studying its decay width, owing to the difference in their molecular components.