qqqq―system in a potential model

Abstract

We have examined the $\mathrm{qq}\overline{\mathrm{qq}}$ system in a nonrelativistic potential model with color-dependent confinement forces and hyperfine interactions by solving the four-particle Schrödinger equation variationally. We find that normally the ground state of this system consists of two free mesons, but that exceptions to this rule probably occur for $K\overline{K}$ systems, where we find weakly bound $0^{++}$ states with a meson-meson structure reminiscent of the nucleon-nucleon structure of the deuteron. We show that these states may be identified with the $S^{*}$ and $\delta$ just below $K\overline{K}$ threshold. We further argue that the $\mathrm{qq}\overline{\mathrm{qq}}$ system is not only nearly barren of bound states, but that it may not support any resonances. Finally, independent of their identification with observed states, we note that the $\mathrm{qq}\overline{\mathrm{qq}}$ bound states are a model for the weak binding and color-singlet clustering observed in nuclei.