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 interaction, were found to increase rapidly with the interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the interaction in the dense nuclear medium are given. Using the Λ(1405) ansatz with a PDG mass of 1405 MeV/c² 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 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.