Representation mixing and exotic baryons in the Skyrme model

We study the effect of representation mixing in the $\mathrm{S}\mathrm{U}(3)$ Skyrme model by diagonalizing exactly the representation-dependent part. It is observed that even without the next-to-leading-order symmetry breaking terms the low-lying baryon masses as well as the recently discovered ${\Theta }^{+}$ and ${\Xi }_{\overline{10}}$ can be fairly well reproduced within 3% accuracy. It is also demonstrated that the mixing effect is not negligible in decay processes of $\{\overline{10}\}$. In particular the effect of mixing with $\{27\}$ is found to be quite large. These results are compatible with the second-order perturbation scheme. The decay widths are found to be sensitive to the mass values. The decay widths of $\{\overline{10}\}$ are estimated to be smaller than those of $\{10\}$ by an order of magnitude due to the destructive interference between operators, although the kinematic factors are comparable.