A model recently introduced by Jaffe and Wilczek based on the quarks being dynamically bound into diquarks has been used to predict that the recently observed exotic baryons (pentaquarks) fall into a nearly ideally mixed combination of the 8 and $\overline{10}$ representations of $\mathrm{S}\mathrm{U}(3)$ flavor. The model predicts two states with nucleon quantum numbers which have tentatively been identified with the ${\mathrm{N}}^{*}(1440)$ and the ${\mathrm{N}}^{*}(1710)$. This paper examines the viability of this model by focusing on the decay width of the nucleon members of the multiplet. An inequality relating the partial widths of these nucleon states in the $\pi +\mathrm{\text{nucleon}}$ channel to the width of the ${\theta }^{+}$ is derived for this model assuming ideal mixing and that the only significant exact $\mathrm{S}\mathrm{U}(3)$ symmetry violations are the result of ideal mixing, threshold effects, and the masses of pseudo-Goldstone bosons. This inequality is badly violated if the states in the multiplet are the ${\mathrm{N}}^{*}(1440)$ and the ${\mathrm{N}}^{*}(1710)$ and if the recent bounds extracted for the ${\theta }^{+}$ width are reliable. Thus, the model appears to require a scenario with the existence of at least one presently unknown resonance with nucleon quantum numbers.

• Received 18 February 2004

DOI:https://doi.org/10.1103/PhysRevD.70.074023