Properties of the baryon antidecuplet

We study the group structure of a baryon antidecuplet containing ${\ensuremath{\Theta}}^{+}.$ We derive the SU(3) mass relations among the pentaquark baryons in the antidecuplet, when there is either no mixing or ideal mixing with the pentaquark octet, as advocated by Jaffe and Wilczek. This constitutes the Gell-Mann--Okubo mass formula for the pentaquark baryons. We also derive the SU(3) symmetric Lagrangian for the interactions of the baryons in the antidecuplet with the meson octet and the baryon octet. Our analysis for the decay widths of the antidecuplet states suggests that $N(1710)$ is ruled out as a pure antidecuplet state, but it may have an antidecuplet component in its wave function if the multiplet is mixed with the pentaquark octet.