Strong binding and shrinkage of single and double [Image: see text] 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 [Image: see text] interaction, were found to increase rapidly with the [Image: see text] interaction strength. Their behaviors are shown in a reference diagram, where possible changes by varying the [Image: see text] 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 [Image: see text] 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.