  In present work, we investigated $K^{-}+\, ^{3}\mathrm{He}$ reaction at low
energies. The coupled-channel Faddeev AGS equations were solved for
$\bar{K}Nd-\pi\Sigma{d}$ three-body system in momentum representation to
extract the scattering amplitudes. To trace the signature of the
$\Lambda$(1405) resonance in the $\pi\Sigma$ invariant mass, the deuteron
energy spectrum for $K^{-}+\,^{3}\mathrm{He}\rightarrow\pi\Sigma{d}$ reaction
was obtained. Different types of $\bar{K}N-\pi\Sigma$ potentials based on
phenomenological and chiral SU(3) approaches were used. As a remarkable result
of this investigation, it was found that the deuteron energy spectrum,
reflecting the $\Lambda$(1405) mass distribution and width, depends quite
sensitively on the $\bar{K}N-\pi\Sigma$ model of interaction. Hence accurate
measurements of the $\pi\Sigma$ mass distribution have the potential to
discriminate between possible mechanisms at work in the formation of the
$\Lambda$(1405).
