We employ two simple and robust results to constrain the mixing matrix of the isosinglet scalar mesons f0(1710), f0(1500), f0(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, f0(1500) becomes a pure SU (3) octet and is degenerate with a0(1450), while f0(1370) is mainly an SU (3) singlet with a slight mixing with the scalar glueball which is the primary component of f0(1710). These features remain essentially unchanged even when SU (3) breaking is taken into account. The observed enhancement of ωf0(1710) production over ɸf0(1710) in hadronic J/ψ decays and the copious f0(1710) production in radiative J/ψ decays lend further support to the prominent glueball nature of f0(1710). We deduce the mass of the pseudoscalar glueball G from an η-η′-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±0.1) GeV, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that η(1405), having a large production rate in the radiative J/ψ decay and not seen in γγ 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.
Mixing among lowest-lying scalar mesons and scalar glueball
