Mixing of Scalar Glueball and Scalar Quarkonia

Abstract

The isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ and their mixing are studied. Two recent lattice results are employed as the starting point; one is the approximate SU(3) symmetry in the scalar sector above 1 GeV for the connected insertion part without $q\bar q$ annihilation, 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 $f_0(1710)$.