Scalar glueball, scalar quarkonia, and their mixing

Abstract

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 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).

Consistent scenario forB→PSdecays

“…Thus, in this approach [2], there is only an small mixing between the singlet and the glueball. Using these values the prediction for B → f 0 (1500)K is in conflict with the experimental data.…”

“…The values reported for the widths marked with * include the corresponding branching of the scalar decaying channel. To obtain the NFA predictions we used B(f0(1370) → 2π) = 0.26(1), B(f0(1500) → 2π) = 0.35 (2) and for the a0(1450) → πη no reliable value exists [3].…”

“…However, even if the experimental data is poor the discrepancy between our results and experimental data is evident, there is a one order of magnitude difference. In this sense it is important to remark that in order to obtain the results of tabler I we assumed, following H. Y. Cheng [2] a mixing between the glueball, singlet and octet components given by: …”

“…The mixing angles seems to be small except by the singlet-glueball which is around −20 o , according to H. Y. Cheng in ref. [2]. It has been more difficult to establish the lighter multiplet, even the existence and nature of some of their members is in doubt.…”

Modelling glueballs

“…The fit to all decays showed the existence of two solutions, one in which f 0 (1500) is predominantly a glueball, and on in which f 0 (1710) is such. Shortly after, Cheng et al [28] also found a phenomenological solution in which f 0 (1710) is predominantly a glueball. Various other studies were performed which involved constituents quarks and gluons, e.g.…”