One- versus two-pole<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi>K</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>N</mml:mi></mml:mrow></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>π</mml:mi><mml:mi>Σ</mml:mi></mml:mrow></mml:math>potential:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>d</mml:mi></mml:mrow></mml:math>scattering length

We investigated the dependence of the ${K}^{\ensuremath{-}}d$ scattering length on models of the $\overline{K}N$ interaction with one or two poles for the $\ensuremath{\Lambda}(1405)$ resonance. The $\overline{K}NN\ensuremath{-}\ensuremath{\pi}\ensuremath{\Sigma}N$ system is described by coupled-channel Faddeev equations in Alt-Grassberger-Sandhas form. Our new two-body $\overline{K}N\ensuremath{-}\ensuremath{\pi}\ensuremath{\Sigma}$ potentials reproduce all existing experimental data on ${K}^{\ensuremath{-}}p$ scattering and kaonic hydrogen atom characteristics. New models of the $\ensuremath{\Sigma}N\ensuremath{-}\ensuremath{\Lambda}N$ interaction were also constructed. Comparison with several approximations, usually used for scattering length calculations, was performed.

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