Phenomenology of spin 3/2 baryons with pentaquarks

Abstract

We examine several assignments of spin and parity for the pentaquark ${\ensuremath{\Theta}}^{+}$ state (${J}^{P}=1/{2}^{\ifmmode\pm\else\textpm\fi{}},3/{2}^{\ifmmode\pm\else\textpm\fi{}}$) in connection with known baryon resonances. Assuming that the ${\ensuremath{\Theta}}^{+}$ belongs to an antidecuplet representation which mixes with an octet, we calculate the mass spectra of the flavor partners of the ${\ensuremath{\Theta}}^{+}$ based on the SU(3) symmetry. The decay widths of the ${\ensuremath{\Theta}}^{+}$ 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 $\ensuremath{\Theta}(1540)$ and ${\ensuremath{\Xi}}_{3/2}(1860)$, when their spin and parity are assigned to be ${J}^{P}=3/{2}^{\ensuremath{-}}$, together with other ${J}^{P}=3/{2}^{\ensuremath{-}}$ resonances. The decay widths of $\ensuremath{\Theta}\ensuremath{\rightarrow}KN$, $N(1520)\ensuremath{\rightarrow}\ensuremath{\pi}N$, and $N(1700)\ensuremath{\rightarrow}\ensuremath{\pi}N$ are also reproduced simultaneously.