Scalar and Pseudoscalar Glueballs

Abstract

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 $ωf_0(1710)$ production over $ϕf_0(1710)$ in hadronic $J/ψ$ decays and the copious $f_0(1710)$ production in radiative $J/ψ$ decays lend further support to the prominent glueball nature of $f_0(1710)$. 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 $(1.4\pm 0.1)$ GeV, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that $η(1405)$, 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.

10 pages, 1 figure; talk presented at "Particle Physics, Astrophysics and Quantum Field Theory: 75 Years since Solvay", November 27-29, 2008, Singapore