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We investigated the dependence of the $K^- d$ scattering length on models of$\bar{K}N$ interaction with one or two poles for $\Lambda(1405)$ resonance. The$\bar{K}NN - \pi \Sigma N$ system is described by coupled-channel Faddeevequations in AGS form. Our new two-body $\bar{K}N - \pi \Sigma$ potentialsreproduce all existing experimental data on $K^- p$ scattering and kaonichydrogen atom characteristics. New models of $\Sigma N - \Lambda N$ interactionwere also constructed. Comparison with several approximations, usually used forscattering length calculations, was performed.

One- versus two-pole $\bar{K}N - \pi \Sigma$ potential: $K^- d$ scattering length