A light collective ${\theta }^{+}$ baryon state (with strangeness +1) was predicted via rigid-rotor collective quantization of SU(3) chiral soliton models. This paper explores the validity of this treatment. A number of rather general analyses suggest that predictions of exotic baryon properties based on this approximation do not follow from large $N_c$ QCD. These include an analysis of the baryon’s width, a comparison of the predictions with general large $N_c$ consistency conditions of the Gervais-Sakita-Dashen-Manohar type; an application of the technique to QCD in the limit where the quarks are heavy; a comparison of this method with the vibration approach of Callan and Klebanov; and the ${1/N}_c$ scaling of the excitation energy. It is suggested that the origin of the problem lies in an implicit assumption in the that the collective motion is orthogonal to vibrational motion. While true for non-exotic motion, the Wess-Zumino term induces mixing at leading order between collective and vibrational motion with exotic quantum numbers. This suggests that successful phenomenological predictions of ${\theta }^{+}$ properties based on rigid-rotor quantization were accidental.

• Received 19 December 2003

DOI:https://doi.org/10.1103/PhysRevD.70.014011