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 admin note: text overlap with arXiv:1710.07424