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

Abstract

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