  It has been recently conjectured by Selem and Wilczek \cite{Sel06} the
existence of a $ss-[\bar u \bar d]$ meson due to strong correlations between
the two light antiquarks. We make a detailed study of this system within a
dynamical quark model which has proven to be successful in reproducing the most
important features of low-energy hadron phenomenology. Our results, obtained
within a parameter-free calculation, show that the antidiquark component of the
$ss \bar u \bar d$ system indeed entails the stronger attraction, and drives
its energy much lower than the $\bar{N}\Xi$ threshold, but still above the
$\bar{K^0} {K^*}^-$ or $\bar{{K^*}^0} K^-$ thresholds. We have also studied the
$cc \bar u \bar d$ and $bb \bar u \bar d$ systems. Exotic mesons are only
expected to exist in the limit of large mass for the two-quark subsystem,
$bb\bar u \bar d$, since the calculated mass is below the $\bar{B^0} {B^*}^-$
or $\bar{{B^*}^0} B^-$ thresholds.
