Quark and glue spectroscopy of scalars and pseudoscalars in SU(3) flavor limit
Within the framework of the generalized linear sigma model with glueballs recently proposed [1,2], we study the schematic spectroscopy of scalar and pseudoscalar mesons in the SU(3) flavor limit and explore their quark and glue contents. In this framework, for both scalars and pseudoscalars, the two octet physical states are admixtures of quark-antiquark and four-quark components, and the three singlet states contain quark-antiquark, four-quark and glue components. We identify the two scalar octets with $a_0(980)$ and $a_0(1450)$ and the two pseudoscalar octets with $π(137)$ and $π(1300)$. We show that, as expected, the light pseudoscalar octet is made dominantly of quark-antiquarks whereas the light scalar octet has a reversed substructure with a dominant four-quark component. The case of singlets is more complex due to surplus of states up to around 2 GeV. We consider all 35 permutations for identifying the three pseudoscalar singlets of our model with three of the seven experimental candidates. Our numerical simulation unambiguously identifies the lightest and the heaviest pseudoscalar singlets with $η(547)$ and $η(2225)$, respectively, and favors the identification of the middle singlet with either $η(1295)$ or $η(1405)$ [or, to a lesser extent, with $η(1475)$] and thereby allows a probe of their substructures. We then estimate the quark and glue components and find that the three pseudoscalar singlets (from lightest to heaviest) are mainly of quark-antiquark, four-quark and glue substructure, while the corresponding three scalar singlets (from lightest to heaviest) are of four-quark, quark antiquark and glue contents. The masses of pure pseudoscalar and scalar glueballs are estimated around 2.0 and 1.6 GeV, respectively.