Dynamical study of the pentaquark antidecuplet

Dynamical calculations are performed for all isomultiplets of the flavour antidecuplet to which the newly discovered pentaquark $\Theta^+$ belongs. The framework is a constituent quark model where the short-range interaction has a flavour-spin structure. In this model the lowest pentaquarks have positive parity. Each antidecuplet member is described by a variational solution with the Pauli principle properly taken into account. By fitting the mass of $\Theta^+$ of minimal content $uudd\bar{s}$, the mass of $\Xi^{--}$, of minimal content $ddss \bar{u}$, is predicted at approximately 1960 MeV. The influence of the octet-antidecuplet mixing on the masses of the $Y = 1$ and 0 pentaquarks is considered within the same model and the role of the kinetic energy plus the hyperfine interaction in this mixing is pointed out.