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 \( Λ(1405) \) 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 \( πΣp \) mass spectrum. This supports the feasibility of observing the \( K^{-}pp \) cluster in low-energy kaon-induced reactions on helium-3.

Figures (4)

• Figure 1: (Color online) Schematic representation of the transition from $K^{-} + \mathrm{^{3}He}$ to $n + (\pi\Sigma p)$ via the intermediate $N + (\bar{K}NN)_{s=0}$ state.
• Figure 2: (Color online) Schematic representation of the transition from $K^{-} + {}^{3}\mathrm{He}$ to $n + (\pi\Sigma p)$ via the intermediate state $N + (\bar{K}NN)_{s=0}$. The large solid ellipse denotes the four-body dynamics of the initial system, while the rectangular box represents the three-body dynamics associated with the formation and decay of the $\bar{K}NN$ cluster.
• Figure 3: (Color online) The neutron missing mass spectrum is presented. In this analysis, the full four-body Faddeev amplitude is not included; instead, only the reaction mechanisms within the region within the dashed ellipse in Fig. \ref{['fig1']} are considered. A clear peak associated with the $K^-pp$ bound state is visible for all interaction models examined. In addition to the $K^-pp$ signal, an enhancement attributed to the $\Lambda(1405)$ resonance appears in the spectrum, particularly when using the SIDD2 and chiral potentials. In contrast, for the SIDD1 potential, the $\Lambda(1405)$ pole lies above the threshold, which is reflected in the corresponding spectral distribution.
• Figure 4: Calculated neutron missing mass spectrum for the $K^- + ^3$He $\rightarrow$$n + (\pi\Sigma p)$ reaction at a kaon momentum of 100 MeV/$c$. The explanations are the same as in Fig. \ref{['fig2']}. Here, the full four-body Faddeev calculations was performed to detemine the neutron mass spectrum.