Investigation of the $K^{-}pp$ Bound State via the \( K^{-} + {}^{3}\mathrm{He} \) Reaction

Abstract

Using the four-body Alt-Grassberger-Sandhas (AGS) equations for the \( K^{-}ppn \) system, we investigate the possible formation of a \( K^{-}pp \) quasi-bound state through the low-energy \( K^{-} + {}^{3}\mathrm{He} \) reaction. The neutron missing mass spectrum in the final state was calculated for different models of the \( \bar{K}N \) interaction. The results indicate that, irrespective of the specific nature of the \( \Lambda(1405) \) structure or the details of the \( \bar{K}N \) interaction model, a signal corresponding to the \( K^{-}pp \) quasi-bound state could appear in the \( \pi \Sigma p \) mass spectrum. This supports the feasibility of observing the \( K^{-}pp \) cluster in low-energy kaon-induced reactions on helium-3.