  We study whether the pseudoscalar glueball mass in full QCD can differ from
the prediction of quenched lattice calculations. Using properties of the
correlator of the vacuum topological susceptibility we derive an expression for
the upper bound on the QCD glueball mass. We show that the QCD pseudoscalar
glueball is lighter than the pure Yang-Mills theory glueball studied in
quenched lattice calculations. The mass difference between those two states is
of order of $1/N_c$. The value calculated for the $0^{-+}$ QCD glueball mass
can not be reconciled with any physical state observed so far in the
corresponding channel. The glueball decay constant and its production rate in
$J/\psi$ radiative decays are calculated. The production rate is large enough
to be studied experimentally.
