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Characteristics of the quasi-bound state in the $K^- pp$ system stronglydepend on the model of antikaon-nucleon interaction and weakly - on thenucleon-nucleon potential. In the present paper, dynamically exact Faddeev-typecalculations with coupled $\bar{K}NN$ and $\pi \Sigma N$ were performed usingdifferent models of the $\Sigma N$ and $\pi N$ interactions to study theinfluence of these "less important" interaction on the three-body result. Inaddition, dynamically exact three-body Faddeev-type AGS calculations with threecoupled particle channels $\bar{K}NN - \pi \Sigma N - \pi \Lambda N$ wereperformed.

Fine-tuning of the quasi-bound $K^- pp$ state