Search and research of K̄NNN and K̄K̄NN antikaonic clusters

This review presents the current status of experimental searches and theoretical studies of antikaonic four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters. Theoretical approaches within the framework of non-relativistic potential models used for the investigation of four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters, such as the variational, Faddeev equations, and hyperspherical harmonics are considered. The results of calculations for the binding energies and the widths obtained within these methods by employing diverse sets of nucleon–nucleon, effective $\bar{K}N$, and antikaon–antikaon interactions are presented, discussed, and compared with the calculations using the method of hyperspherical harmonics in momentum representation. The presented results demonstrate that the quasibound state energy of antikaonic four-body $\bar{K}NNN$ and $\bar{K}\bar{K}NN$ clusters is not sensitive to the $NN$ interaction, and show a very strong dependence on the $\bar{K}N$ potential. Despite the strong short-range repulsion due to the $NN$ interaction in $K^{-}ppp$ and $K^{-}{K}^{-}pp$ and the weak $\bar{K}\bar{K}$ repulsion in $K^{-}{K}^{-}pp$, the antikaonic clusters $K^{-}ppp$ and $K^{-}{K}^{-}pp$ are strongly bound.