Isospin mixing effects in the low-energy<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:mtext>−</mml:mtext><mml:mi>π</mml:mi><mml:mi>Σ</mml:mi></mml:mrow></mml:math>interaction

New strong coupled-channels $\overline{K}N\text{\ensuremath{-}}\ensuremath{\pi}\ensuremath{\Sigma}$ potential, reproducing all existing experimental data and suitable for using in an accurate few-body calculations, is constructed. Isospin breaking effects of direct inclusion of the Coulomb interaction and using of physical masses in calculations are investigated. The $1s$ level shift and width of kaonic hydrogen, consistent with the scattering data, was obtained and the corresponding exact strong ${K}^{\ensuremath{-}}p$ scattering length was calculated. One- and two-pole form of $\ensuremath{\Lambda}(1405)$ resonance was considered.

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