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Within the framework of the generalized linear sigma model with glueballsrecently proposed [1,2], we study the schematic spectroscopy of scalar andpseudoscalar mesons in the SU(3) flavor limit and explore their quark and gluecontents. In this framework, for both scalars and pseudoscalars, the two octetphysical states are admixtures of quark-antiquark and four-quark components,and the three singlet states contain quark-antiquark, four-quark and gluecomponents. We identify the two scalar octets with $a_0(980)$ and $a_0(1450)$and the two pseudoscalar octets with $\pi(137)$ and $\pi(1300)$. We show that,as expected, the light pseudoscalar octet is made dominantly ofquark-antiquarks whereas the light scalar octet has a reversed substructurewith a dominant four-quark component. The case of singlets is more complex dueto surplus of states up to around 2 GeV. We consider all 35 permutations foridentifying the three pseudoscalar singlets of our model with three of theseven experimental candidates. Our numerical simulation unambiguouslyidentifies the lightest and the heaviest pseudoscalar singlets with $\eta(547)$and $\eta(2225)$, respectively, and favors the identification of the middlesinglet with either $\eta(1295)$ or $\eta(1405)$ [or, to a lesser extent, with$\eta(1475)$] and thereby allows a probe of their substructures. We thenestimate the quark and glue components and find that the three pseudoscalarsinglets (from lightest to heaviest) are mainly of quark-antiquark, four-quarkand glue substructure, while the corresponding three scalar singlets (fromlightest to heaviest) are of four-quark, quark antiquark and glue contents. Themasses of pure pseudoscalar and scalar glueballs are estimated around 2.0 and1.6 GeV, respectively.

Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit