QCD tests of the puzzling scalar mesons

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals (q¯q, q¯q¯qq, and gluonium) for the nature of scalar mesons. In the I=1 and 1/2 channels, the unusual wrong splitting between the a₀(980) and κ(900) and the a₀(980) width can be understood from QSSR within a q¯q assignment. However, none of the q¯q and q¯q¯qq results can explain the large κ 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 σ_B(1GeV) coupled strongly to Goldstone boson pairs which plays in the U(1)_V channel, a similar role as the η^' for the value of the U(1)_A topological charge. The observed σ(600) and f₀(980) mesons result from a maximal mixing between the gluonium σ_B and q¯q (1 GeV) mesons, a mixing scheme which passes several experimental tests. Okubo-Zweig-Izuki (OZI) violating J/ψ→ϕπ⁺π^-, D_s→3π decays, and J/ψ→γS glueball filter processes may indicate that the f₀(1500), f₀(1710), and f₀(1790) have significant gluonium components in their wave functions, while the f₀(1370) is mostly q¯q. Tests of these results can be provided by the measurements of the pure gluonium η^'η and 4π specific U(1)_A decay channels.