Exact calculations of a quasibound state in the (K)over-bar (K)over-bar N system

Dynamically exact calculations of a quasibound state in the (K) over bar (K) over bar N three-body system are performed using Faddeev-type AGS equations. As input two phenomenological and one chirally motivated (K) over bar N potentials are used, which describe the experimental information on the (K) over bar N system equally well and produce either a one- or two-pole structure of the Lambda (1405) resonance. For the (K) over bar (K) over bar interaction separable potentials are employed that are fitted to phase shifts obtained from two theoretical models. The first one is a phenomenological (K) over bar (K) over bar potential based on meson exchange, which is derived by SU(3) symmetry arguments from the Julich pi pi - (K) over bar K coupled-channels model. The other interaction is a variant of the first one, which is adjusted to the K K s-wave scattering length recently determined in lattice QCD simulations. The position and width of the (K) over bar (K) over bar 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. Aquasibound state is found with binding energy B ((K) over bar (K) over bar N) = 12-26 MeV and width Gamma((K$) over bar (K) over bar N) (=) 61-102 MeV, which could correspond to the experimentally observed Xi (1950) state.