Binding of antikaons and Lambda(1405) clusters in light kaonic nuclei

Abstract

The energy spectra of light-mass kaonic nuclei were investigated using the theoretical framework of the $0s$-orbital model with zero-range $\bar{K}N$ and $\bar{K}\bar{K}$ interactions of effective single-channel real potentials. The energies of the $\bar{K}NN$, $\bar{K}NNN$, $\bar{K}NNNN$, $\bar{K}\bar{K}N$, and $\bar{K}\bar{K}NN$ systems were calculated in the cases of weak- and deep-binding of the $\bar{K}N$ interaction, which was adjusted to fit the $\Lambda (1405)$ mass with the energy of the $\bar{K}N$ bound state. The results qualitatively reproduced the energy systematics of kaonic nuclei calculated via other theoretical approaches. In the energy spectra of the $\bar{K}NN$ and $\bar{K}\bar{K}NN$ systems, the lowest states $\bar{K}NN(J^{\pi },T=0^{-},1/2)$ and $\bar{K}\bar{K}NN(0^{+},0)$ were found to have binding energies approximately twice and four times as large as that of the $\bar{K}N(1/2^{-},0)$ state, respectively. Higher $(J^{\pi },T)$ states including $\bar{K}NN(1^{-},1/2)$, $\bar{K}\bar{K}NN(0^{+},1)$, and $\bar{K}\bar{K}NN(1^{+},1)$ were predicted at energies of 9--25 MeV below the antikaon-decay threshold. The effective $\Lambda (1405)$-$\Lambda (1405)$ interaction in the $\bar{K}\bar{K}NN$ system was also investigated via a $\bar{K}N+\bar{K}N$-cluster model. Strong and weak $\Lambda (1405)$-$\Lambda (1405)$ attractions were obtained in the $S^{\pi }=0^{+}$ and $S^{\pi }=1^{-}$ channels, respectively. The $\Lambda (1405)$-$\Lambda (1405)$ interaction in the $$\bar{K}\bar{K}NN$ system was compared with the effective $d$-$d$ interaction in the $NNNN$ system, and the properties of dimer-dimer interactions in hadron and nuclear systems were discussed.

Comments: 16 pages, 4 figures