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

In this work, we assume that the observed state $Xi(1620)$ is a $s$-wave $Lambdabar{K}$ or $Sigmabar{K}$ 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 $Lambdabar{K}$ and $Sigmabar{K}$ systems numerically and find that the $Xi(1620)$ can be explained as $Lambdabar{K}$ and $Sigmabar{K}$ bound states with $J^P=1/2^-$, respectively. Then we calculate the decay widths of $Xi(1620)rightarrowXipi$ in these two different molecule pictures systems, respectively.