Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals ($\overline{q}q$, $\overline{q}\overline{q}qq$, and gluonium) for the nature of scalar mesons. In the $I=1$ and $1/2$ channels, the unusual wrong splitting between the $a_0(980)$ and $\kappa (900)$ and the $a_0(980)$ width can be understood from QSSR within a $\overline{q}q$ assignment. However, none of the $\overline{q}q$ and $\overline{q}\overline{q}qq$ results can explain the large $\kappa$ width, which may suggest that it can result from a strong interference with nonresonant backgrounds. In the $I=0$ channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium ${\sigma }_B(1\mathrm{GeV})$ coupled strongly to Goldstone boson pairs which plays in the $U(1{)}_V$ channel, a similar role as the ${\eta }^{\prime }$ for the value of the $U(1{)}_A$ topological charge. The observed $\sigma (600)$ and $f_0(980)$ mesons result from a maximal mixing between the gluonium ${\sigma }_B$ and $\overline{q}q$ (1 GeV) mesons, a mixing scheme which passes several experimental tests. Okubo-Zweig-Izuki (OZI) violating $J/\psi \to \varphi {\pi }^{+}{\pi }^{-}$, $D_s\to 3\pi$ decays, and $J/\psi \to \gamma S$ glueball filter processes may indicate that the $f_0(1500)$, $f_0(1710)$, and $f_0(1790)$ have significant gluonium components in their wave functions, while the $f_0(1370)$ is mostly $\overline{q}q$. Tests of these results can be provided by the measurements of the pure gluonium ${\eta }^{\prime }\eta$ and $4\pi$ specific $U(1{)}_A$ decay channels.

• Received 13 April 2006

DOI:https://doi.org/10.1103/PhysRevD.73.114024