Mixing of Pentaquark and Molecular States

There are experimental evidences for the existence of narrow states $\Theta^+$ and $\Theta_c$ with the same quantum numbers of $uudd\bar s$ and $uudd\bar c$ pentaquarks and also $NK^{(*)}$ and $ND^{(*)}$ molecular states. Their masses deviate from many theoretical estimates of the pure pentaquark and molecular states. In this work we study the possibility that the observed $\Theta^+$ and $\Theta_c$ are mixtures of pure pentaquark and molecular states. The mixing parameters are in general related to non-perturbative QCD which are not calculable at present. We determine them by fitting data from known states and then generalize the mechanism to $\Theta_b$ to predict its mass and width. The mixing mechanism can also naturally explain the narrow width for $\Theta^+$ and $\Theta_c$ through destructive interferences, even if the pure pentaquark and molecular states have much larger decay widths. We also briefly discuss the properties of the partner eigenstates of $\Theta^+$ and $\Theta_c$ and the possibility of experimentally observe them. Moreover, probable consequences of multi-state mixing are also addressed.