Schematic model for QCD. III. Hadronic states

The hadronic spectrum obtained in the framework of a QCD-inspired schematic model is presented. The model is the extension of a previous version, whose basic degrees of freedom are constituent quarks, antiquarks, and gluons. The interaction between quarks and gluons is a phenomenological interaction and its parameters are fixed from data. The classification of the states, in terms of quark and antiquark and gluon configurations is based on symmetry considerations, and it is independent of the chosen interaction. Following this procedure, nucleon and $\Delta$ resonances are identified, as well as various penta- and hepta-quarks states. The lowest pentaquarks state is predicted at $1.5\mathrm{GeV}$ and it has negative parity, while the lowest hepta-quarks state has positive parity and its energy is of the order of $2.5\mathrm{GeV}$.

Figure 1

Schematic representation of the model space. The fermion levels are indicated by their energies $\pm {\omega }_f$. The gluon-pairs are represented by the level at the energy ${\omega }_b$.

Figure 2

Nucleon resonances (first group of levels), $\Delta$ resonances (second group), pentaquarks (third group), and heptaquarks (fourth group). At the right side of each level are given the assigned spin and parity $\left(J^{\pi }\right)$, and the total quark and antiquark $\left(n_q+n_{\overline{q}}\right)$ and gluon $\left(n_g\right)$ contents (see the text) The list is not complete. Only some selected states, of physical interest, are listed.