  We present a generalized linear sigma model that includes both scalar and
pseudoscalar glueballs in addition to a quark-antiquark as well as a four-quark
chiral nonet. Utilizing the axial and trace anomalies of QCD (at the effective
mesonic level), we aim to develope the most general structure of the Lagrangian
which can be used to study the interaction of quarkonia with glueballs. We then
study the effect of scalar glueball on the vacuum of the model by considering a
decoupling limit in which the glueball fields are decoupled from quarkonia.
This determines the properties of the pure scalar glueball and builds a
practical foundation for determining the model parameters when the interactions
are turned on.
