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

在目前的工作中，我们研究了低能量下的\（K ^ {-} + \，^ {3} \ mathrm {He} \）反应。对动量表示中的\（{\ bar {K}} Nd- \ pi \ varSigma {d} \）三体系统求解耦合通道Faddeev AGS方程，以提取散射振幅。为了跟踪\（\ pi \ varSigma \）不变质量中\（\ varLambda \）（1405）共振的特征，\（K ^ {-} + \，^ {3} \ mathrm的氘核能谱获得{He} \ rightarrow \ pi \ varSigma {d} \）反应。不同类型的\（{\ bar {K}} N- \ pi \ varSigma \）使用基于现象学和手性SU（3）方法的潜力。作为这项研究的显著结果，发现氘核能谱反映了\（\ varLambda \）（1405）的质量分布和宽度，非常敏感地取决于\（{\ bar {K}} N- \ pi \ varSigma \）交互模型。因此，对\（\ pi \ varSigma \）质量分布的精确测量有可能在\（\ varLambda \）的形成中区分可能起作用的机制（1405）。