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One of the most important characteristics of a two-body interaction is existence  and properties of its bound states or resonances. When the interaction is used  in a few- or many-body calculation they also strongly inuence the properties of  the few- or many-body system. We investigate the dependence of the three-body  resonance properties in the $ar{K}$NN system on the dierent models  of $ar{K}$N interaction, providing one or two poles for  Λ(1405) resonance. The $ar{K}$NN − πΣN system is described by coupled-channel Faddeev equations in AGS  form, our two-body $ar{K}$N − πΣ interaction models  reproduce all existing experimental data on K−  p scattering and K−  p atom level shift

Two- and three-body resonances in the $\bar{K}$NN−πΣNsystem