Spinless glueballs in generalized linear sigma model

Within the framework of the generalized linear sigma model, a comprehensive analysis of scalar and pseudoscalar glueballs and their mixing with mesons is presented. The Lagrangian of the model contains two chiral nonets, a quark-antiquark type and a two-quark two-antiquark type. The pseudoscalar and scalar glueballs are introduced through their connections with the axial and the trace anomalies of QCD, respectively. It is found that in order to satisfy the axial anomaly and at the same time accurately generate all seven eta masses, it is necessary to include at least two pseudoscalar glueballs, a physical one and an unphysical one that gets integrated out and yields an effective instanton-type term which is needed in generation of the eta masses. At the leading order, which corresponds to keeping effective terms in the Lagrangian that contain no more than eight underlying quarks and antiquarks, the mass spectrum of the model is worked out and shown to be in complete agreement with experiment. The quark and glue contents of the isosinglet scalars below 2 GeV, and of the isosinglet pseudoscalars up to around 2.2 GeV, are analyzed in detail and their correlations with the scalar glueball condensate are examined. Decay widths of isosinglet scalars as well as different self consistencies within this framework are used to probe the glueball condensate and thereby estimate the quark and glue contents of these states. In the pseudoscalar sector, the state that is dominantly made of glue is clearly a state with mass above 2 GeV. In the scalar sector, the identification of glue contents is less certain and in principle the three isosinglets in the 1.5-2.0 GeV can contain substantial glue. These glue contents are determined as functions of the scalar glueball condensate which is the key quantity in this analysis.