  After discussing the OZI suppression of one light meson exchange in the
interaction of $D^* \bar D^*$ with isospin I=1, we study the contribution of
two pion exchange to the interaction and the exchange of a heavy vector
$J/\psi$. We find this latter mechanism weak but enough to barely bind the
system in J=2 with a mass around 4000 MeV, while the effect of the two pion
exchange is a net attraction but weaker than that from $J/\psi$ exchange. We
discuss this state and try to relate it to the $Z_c(4025)$ state, above the
$D^* \bar D^*$ threshold, claimed in an experiment at BES from and enhancement
of the $D^* \bar D^*$ distribution close to threshold. Together with the
results from a recent reanalysis of the BES experiment showing that it is
compatible with a J=2 state below threshold around 3990 MeV, we conclude that
the BES experiment could be showing the existence of the state that we find in
our approach.
