Strong binding and shrinkage of single and double nuclear systems (K−pp, K−ppn, K−K−p and K−K−pp) predicted by Faddeev-Yakubovsky calculations

Non-relativistic Faddeev and Faddeev-Yakubovsky calculations were made for K(-)pp, K(-)ppn, K(-)K(-)p and K(-)K(-)pp kaonic nuclear clusters, where the quasi bound states were treated as bound states by employing real separable potential models for the K(-)-K(-) and the K(-)-nucleon interactions as well as for the nucleon-nucleon interaction. The binding energies and spatial shrinkages of these states, obtained for various values of the K interaction, were found to increase rapidly with the K interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the K interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c(2) for K(-)p, the following ground-state binding energies together with the wave functions were obtained: 51.5 MeV (K(-)pp), 69 MeV (K(-)ppn), 30.4 MeV (K(-)K(-)p) and 93 MeV (K(-)K(-)pp), which are in good agreement with previous results of variational calculation based on the Akaishi-Yamazaki coupled-channel potential. The K(-)K(-)pp state has a significantly increased density where the two nucleons are located very close to each other, in spite of the inner NN repulsion. Relativistic corrections on the calculated non-relativistic results indicate substantial lowering of the bound-state masses, especially of K(-)K(-)pp, toward the kaon condensation regime. The fact that the recently observed binding energy of K(-)pp is much larger (by a factor of 2) than the originally predicted one may infer an enhancement of the K interaction in dense nuclei by about 25% possibly due to chiral symmetry restoration. In this respect some qualitative accounts are given based on "clearing QCD vacuum" model of Brown, Kubodera and Rho.