  We employ two simple and robust results to constrain the mixing matrix of the
isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$: one is the
approximate SU(3) symmetry empirically observed in the scalar sector above 1
GeV and confirmed by lattice QCD, and the other is the scalar glueball mass at
1710 MeV in the quenched approximation. In the SU(3) symmetry limit,
$f_0(1500)$ becomes a pure SU(3) octet and is degenerate with $a_0(1450)$,
while $f_0(1370)$ is mainly an SU(3) singlet with a slight mixing with the
scalar glueball which is the primary component of $f_0(1710)$. These features
remain essentially unchanged even when SU(3) breaking is taken into account.
The observed enhancement of $\omega f_0(1710)$ production over $\phi f_0(1710)$
in hadronic $J/\psi$ decays and the copious $f_0(1710)$ production in radiative
$J/\psi$ decays lend further support to the prominent glueball nature of
$f_0(1710)$. We deduce the mass of the pseudoscalar glueball $G$ from an
$\eta$-$\eta'$-$G$ mixing formalism based on the anomalous Ward identity for
transition matrix elements. With the inputs from the recent KLOE experiment, we
find a solution for the pseudoscalar glueball mass around $(1.4\pm 0.1)$ GeV,
which is fairly insensitive to a range of inputs with or without
Okubo-Zweig-Iizuka-rule violating effects. This affirms that $\eta(1405)$,
having a large production rate in the radiative $J/\psi$ decay and not seen in
$\gamma\gamma$ reactions, is indeed a leading candidate for the pseudoscalar
glueball. It is much lower than the results from quenched lattice QCD ($>2.0$
GeV) due to the dynamic fermion effect. It is thus urgent to have a full QCD
lattice calculation of pseudoscalar glueball masses.
