The 27-plet baryons with spin 3/2 under SU(3) symmetry

We investigate the spin 3/2 baryons in the 27-plet based on flavor SU(3) symmetry. For $J^p=3/2^+$, we find all the candidates for non-exotic members. For $J^p=3/2^-$, we predict a new non-exotic member $\Lambda(1780)$. Fitting the mass spectrum and calculating the widths of the members show an approximate symmetry of the 27-plet of SU(3). We find that the exotic members have relatively large widths and the $\Xi(1950)$ has spin and parity $J^p=3/2^-$. The possibility of assigning the non-exotic candidates to an octet is also analyzed.