QCD tests of the puzzling scalar mesons

Abstract

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 $\ensuremath{\kappa}(900)$ 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 $\ensuremath{\kappa}$ 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 ${\ensuremath{\sigma}}_{B}(1\text{ }\text{ }\mathrm{GeV})$ coupled strongly to Goldstone boson pairs which plays in the $U(1{)}_{V}$ channel, a similar role as the ${\ensuremath{\eta}}^{\ensuremath{'}}$ for the value of the $U(1{)}_{A}$ topological charge. The observed $\ensuremath{\sigma}(600)$ and ${f}_{0}(980)$ mesons result from a maximal mixing between the gluonium ${\ensuremath{\sigma}}_{B}$ and $\overline{q}q$ (1 GeV) mesons, a mixing scheme which passes several experimental tests. Okubo-Zweig-Izuki (OZI) violating $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${D}_{s}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decays, and $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}S$ 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 ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\eta}$ and $4\ensuremath{\pi}$ specific $U(1{)}_{A}$ decay channels.