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The pseudoscalar meson and baryon octet interaction with strangeness $S=-2$ in the unitary coupled-channel approximation

The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the infinite and finite volume respectively. It is found that there is a resonance state generated dynamically, which owns a mass about 1550MeV and a large decay width of 120-200MeV. This resonance state couples strongly to the $πΞ$ channel. Therefore, it might not correspond to the $Ξ(1620)$ particle announced by Belle collaboration. At the same time, this problem is studied in the finite volume, and an energy level at 1570MeV is obtained, which is between the $πΞ$ and $\bar{K}Λ$ thresholds and independent of the cubic box size.