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

Abstract

In this work, we assume that the observed state Ξ(1620) is a s-wave ΛK or ΣK bound state. Based on this molecule picture, we establish the Bethe-Salpeter equations for Ξ(1620) in the ladder and instantaneous approximations. We solve the Bethe-Salpeter equations for the ΛK and ΣK systems numerically and find that the Ξ (1620) can be explained as ΛK and ΣK bound states with J P = 1/2 − , respectively. Then we calculate the decay widths of Ξ(1620) → Ξπ in these two different molecule pictures systems, respectively.

K¯Λ molecular explanation to the newly observed Ξ(1620)0Chen1, Chen2, Sun3 et al. 2019Phys. Rev. D150151View full textAdd to dashboardCite

“…[22,23], the Ξð1620Þ was interpreted as a J P ¼ 1=2 − resonance dynamically generated in chiral unitary approach. By introducing the vector exchange interaction, the Bethe-Salpeter equation approach [24] was applied to identify the Ξð1620Þ as aKΛ or aKΣ molecular state.…”

Radiative decay of the $Ξ(1620)$ in a hadronic molecule picture

“…As indicated in Refs. [8][9][10][11][12][13][14][15], the Ξ(1620) can be understood as a molecular state in comparison with the Belle data [2]. A molecular state with a narrow width and a mass around 1606 MeV was predicted in the unitarized coupled channels approach [8][9][10][11].…”

“…A possible explanation for these results of Refs. [8][9][10][11]14] is that the Ξ(1620) has a larger KΛ component [13,15]. Moreover, the KΣ component can not be underestimated to reproduce the total decay width of the Ξ(1620) and a study of the spectroscopy alone does not give a complete picture of its nature [15].…”

Strong decays of the $Ξ(1620)$ as a $Λ\bar{K}$ and $Σ\bar{K}$ molecule

“…Following the discovery of the Ξ(1620), several theoretical studies have been performed [13,14]. In the Bethe-Salpeter equation approach under the ladder and instantaneous approximations, based on the analysis of the mass spectrum and the two-body strong decays, the Ξ(1620) is explained as KΛ or Σ K bound states with spin-parity [13]. We note that the decay widths are 36.94 MeV and 9.35 MeV for the KΛ and Σ K bound states, respectively.…”