Baryon resonances in the mean field approach and a simple explanation of the $\Theta^+$ pentaquark

We suggest to classify baryon resonances as single-quark states in a mean field, and/or as its collective excitations. Identifying the Roper resonance $N(1440,{\textstyle{\frac12}}^+)$, the nucleon resonance $N(1535,{\textstyle{\frac12}}^-)$, and the singlet hyperon $\Lambda(1405,{\textstyle{\frac12}}^-)$ as single-quark excitations, we find that there must be an exotic $S=+1$ baryon resonance $\Theta^+\,$ (the “pentaquark”) with a mass about $1440+1535-1405=1570$ MeV and spin-parity ${\textstyle{\frac12}}^+$. We argue that $\Theta^+\,$ is an analog of the Gamov–Teller excitation long known in nuclear physics.