<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mi mathvariant="italic">NN</mml:mi></mml:mrow></mml:math>quasibound state and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mi>N</mml:mi></mml:mrow></mml:math>interaction: Coupled-channels Faddeev calculations of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mi mathvariant="italic">NN</mml:mi><mml:mtext>−</mml:mtext><mml:mi>π</mml:mi><mml:mi>Σ</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math>system

Coupled-channels three-body calculations of an $I=1/2,{J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$ $\overline{K}\mathit{NN}$ quasibound state in the $\overline{K}\mathit{NN}\text{\ensuremath{-}}\ensuremath{\pi}\ensuremath{\Sigma}N$ system were performed and the dependence of the resulting three-body energy on the two-body $\overline{K}N\text{\ensuremath{-}}\ensuremath{\pi}\ensuremath{\Sigma}$ interaction was investigated. Earlier results of binding energy ${B}_{{K}^{\ensuremath{-}}\mathit{pp}}~50\text{\ensuremath{-}}70$ MeV and width ${\ensuremath{\Gamma}}_{{K}^{\ensuremath{-}}\mathit{pp}}~100$ MeV are confirmed [N. V. Shevchenko et al., Phys. Rev. Lett. 98, 082301 (2007)]. It is shown that a suitably constructed energy-independent complex $\overline{K}N$ potential gives a considerably shallower and narrower three-body quasibound state than the full coupled-channels calculation. Comparison with other calculations is made.

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