Phenomenology of spin 3/2 baryons with pentaquarks

We examine several assignments of spin and parity for the pentaquark $\Theta^+$ state ($J^P=1/2^{\pm}, 3/2^{\pm}$) in connection with known baryon resonances. Assuming that the $\Theta^+$ belongs to an antidecuplet representation which mixes with an octet, we calculate the mass spectra of the flavor partners of the $\Theta^+$ based on the SU(3) symmetry. The decay widths of the $\Theta^+$ and nucleon partners are analyzed for the consistency check of the mixing angle obtained from the masses. It is found that a suitable choice of the mixing angle successfully reproduces the observed masses of $\Theta(1540)$ and $\Xi_{3/2}(1860)$, when their spin and parity are assigned to be $J^P=3/2^-$, together with other $J^P=3/2^-$ resonances. The decay widths of $\Theta\to KN$, $N(1520)\to \pi N$, and $N(1700)\to \pi N$ are also reproduced simultaneously.