Trace of $Λ(1405)$ resonance in low energy $K^{-}+\, ^{3}\mathrm{He}\rightarrow (π^{0}Σ^{0})+d$ reaction
In present work, we investigated $K^{-}+\, ^{3}\mathrm{He}$ reaction at low energies. The coupled-channel Faddeev AGS equations were solved for $\bar{K}Nd-πΣ{d}$ three-body system in momentum representation to extract the scattering amplitudes. To trace the signature of the $Λ$(1405) resonance in the $πΣ$ invariant mass, the deuteron energy spectrum for $K^{-}+\,^{3}\mathrm{He}\rightarrowπΣ{d}$ reaction was obtained. Different types of $\bar{K}N-πΣ$ 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 $Λ$(1405) mass distribution and width, depends quite sensitively on the $\bar{K}N-πΣ$ model of interaction. Hence accurate measurements of the $πΣ$ mass distribution have the potential to discriminate between possible mechanisms at work in the formation of the $Λ$(1405).