Proximity of f0(1500) and f0(1710) to the scalar glueball

Within a nonlinear chiral Lagrangian framework, the underlying mixings among quark-antiquark, four-quark and glue components of f(0)(1500) and f(0)(1710) are studied in a global picture that includes all isosinglet scalar mesons below 2 GeV. The quark components are introduced in the Lagrangian in terms of two separate nonets (a quark-antiquark nonet and a four-quark nonet) which can mix with each other and with a scalar glueball. An iterative Monte Carlo simulation is developed to study the 14 free parameters of the Lagrangian by a simultaneous fit to more than 20 experimental data and constraints on the mass spectrum, decay widths, and decay ratios of the isosinglet scalars below 2 GeV. Moreover, constraints on the mass spectrum and decay widths of isodoublet and isovector scalars below 2 GeV as well as pion-pion scattering amplitude are also taken into account. In the leading order of the model and within the overall experimental uncertainties, the ranges of variation of the model parameters are determined. This leads to a set of points in the 14-dimensional parameter space at which the overall disagreement with experiment is no larger than the overall experimental uncertainties. The insights gained in this global picture, due to the complexities of the mixings as well as the experimental uncertainties, are mainly qualitative but are relatively robust, and reveal that the lowest scalar glueball hides between f(0)(1500) and f(0)(1710), resulting in a considerable mixing with various quark components of these two states. The overall current experimental and theoretical uncertainties do not allow us to pin down the exact glue components of isosinglet states; nevertheless it is shown that the f(0)(1500) and f(0)(1710) have the highest glue component. While this global study does not allow precision predictions for each individual state, it provides useful family correlations among the isosinglet states that are found insightful in probing the substructure of scalars, in general, and the isosinglets, in particular. Specifically, a close correlation between the substructure of isosinglets below and above 1 GeV is observed. It is shown that as the simulations approach the limit where the f(0)(500) and f(0)(980) become the two isosinglet members of an ideally mixed two-quark two-antiquark nonet (which is widely believed to be a good approximation), the f(0)(1500) develops a large glue component. The overall estimate of the scalar glueball mass is found to be 1.58 +/- 0.18 GeV.