Modeling pentaquark and heptaquark states

A schematic model for hadronic states, based on constituent quarks and antiquarks and gluon pairs, is discussed. The phenomenological interaction between quarks and gluons is QCD motivated. The obtained hadronic spectrum leads to the identification of nucleon and $\Delta$ resonances and to pentaquark and heptaquark states. The predicted lowest pentaquark state $\left(J^{\pi }={\frac{1}{2}}^{-}\right)$ lies at the energy of $1.5\mathrm{GeV}$ and it is associated to the observed ${\Theta }^{+}\left(1540\right)$ state. For heptaquarks $\left(J^{\pi }={\frac{1}{2}}^{+},{\frac{3}{2}}^{+}\right)$ the model predicts the lowest state at $2.5\mathrm{GeV}$.

Figure 1

Nucleon resonances (first group of levels), $\Delta$ resonances (second group), pentaquarks (third group) and heptaquarks (fourth group). On the right side of each level are given the assigned spin and parity ($J^{\pi }$), and the total quark and antiquark $\left(n_q+n_{\overline{q}}\right)$ and gluon ($n_g$) contents (see the text).