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

TL;DR

This study uses a theoretical model to explore the binding energies and structures of light kaonic nuclei, revealing significant binding and interactions involving Lambda(1405) clusters, with results aligning qualitatively with other approaches.

Contribution

It introduces a zero-range orbital model to analyze light kaonic nuclei and investigates Lambda(1405) interactions, providing new insights into their energy spectra and cluster interactions.

Findings

Lowest states have binding energies twice and four times larger than the single $ar{K} N$ state.

Predicted higher states are 9-25 MeV below decay threshold.

Strong and weak $ ext{Lambda}(1405)$-$ ext{Lambda}(1405)$ attractions in different channels.

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 $\bar{K}\bar{K} N N$ 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.