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).
Categories: nucl-th