Proximity of f_{0}(1500 ) and f_{0}(1710 ) to the scalar glueball
Abstract
Within a nonlinear chiral Lagrangian framework, the underlying mixings among quarkantiquark, fourquark 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 quarkantiquark nonet and a fourquark 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 pionpion 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 14dimensional 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 twoquark twoantiquark 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 .
 Publication:

Physical Review D
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevD.92.113003
 arXiv:
 arXiv:1511.02449
 Bibcode:
 2015PhRvD..92k3003F
 Keywords:

 14.80.Bn;
 11.30.Rd;
 12.39.Fe;
 Standardmodel Higgs bosons;
 Chiral symmetries;
 Chiral Lagrangians;
 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment;
 High Energy Physics  Lattice;
 Nuclear Theory
 EPrint:
 Journal ref added, Refs updated