Broken $\mathrm{SU}\left(3\right)\mathrm{}$ antidecuplet for ${\Theta }^{+}$ and ${\Xi }_{3/2}$

If the narrow exotic baryon resonances ${\Theta }^{+}\mathrm{}\left(1540\right)\mathrm{}$ and ${\Xi }_{3/2}\mathrm{}\left(1862\right)\mathrm{}$ are members of the $J^P={\frac{1}{2}}^{+}$ antidecuplet with $N^{*}\mathrm{}\left(1710\right),$ the octet-antidecuplet mixing is required not only by the mass spectrum but also by the decay pattern of $N^{*}\mathrm{}\left(1710\right).$ This casts doubt on the validity of the ${\Theta }^{+}$ mass prediction by the chiral soliton model. While all pieces of the existing experimental information point to a small octet-decuplet mixing, the magnitude of mixing required by the mass spectrum is not consistent with the value needed to account for the hadronic decay rates. The discrepancy is not resolved even after the large experimental uncertainty is taken into consideration. We fail to find an alternative $\mathrm{SU}\left(3\right)\mathrm{}$ assignment even with a different spin-parity assignment. When we extend the analysis to mixing with a higher $\mathrm{SU}\left(3\right)\mathrm{}$ multiplet, we find one experimentally testable scenario in the case of mixing with a 27-plet.