Exact calculations of a quasibound state in theK¯K¯Nsystem

Abstract

Dynamically exact calculations of a quasibound state in the $\overline{K}\overline{K}N$ three-body system are performed using Faddeev-type AGS equations. As input two phenomenological and one chirally motivated $\overline{K}N$ potentials are used, which describe the experimental information on the $\overline{K}N$ system equally well and produce either a one- or two-pole structure of the $\mathrm{\ensuremath{\Lambda}}(1405)$ resonance. For the $\overline{K}\overline{K}$ interaction separable potentials are employed that are fitted to phase shifts obtained from two theoretical models. The first one is a phenomenological $\overline{K}\overline{K}$ potential based on meson exchange, which is derived by SU(3) symmetry arguments from the J\"ulich $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{-}\overline{K}K$ coupled-channels model. The other interaction is a variant of the first one, which is adjusted to the $KK s$-wave scattering length recently determined in lattice QCD simulations. The position and width of the $\overline{K}\overline{K}N$ quasibound state is evaluated in two ways: (i) by a direct pole search in the complex energy plane and (ii) using an ``inverse determinant'' method, where one needs to calculate the determinant of the AGS system of equations only for real energies. A quasibound state is found with binding energy ${B}_{\overline{K}\overline{K}N}=12\text{--}26$ MeV and width ${\mathrm{\ensuremath{\Gamma}}}_{\overline{K}\overline{K}N}=61\text{--}102$ MeV, which could correspond to the experimentally observed $\mathrm{\ensuremath{\Xi}}(1950)$ state.