Scalar Glueball, Scalar Quarkonia, and their Mixing

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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16 pages; add discussions on the justification of the lattice results as input for this work, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.74.094005

The isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ and their mixing are studied. We employ two recent lattice results as the starting point; one is the isovector scalar meson $a_0(1450)$ which displays an unusual property of being nearly independent of quark mass for quark masses smaller than that of the strange, and the other is the scalar glueball mass at 1710 MeV in the quenched approximation. In the SU(3) symmetry limit, $f_0(1500)$ turns out to be 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. We discuss the sources of SU(3) breaking and their consequences on flavor-dependent decays of these mesons. 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 $f_0(1710)$.

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