Masses, decays and mixings of gluonia in QCD

Abstract

We compute the masses and decay widths of gluonia using QCD spectral sum rules and low-energy theorems. In the scalar sector, one finds a gluonium having a mass $M_G=(1.5\pm 0.2)$ GeV, which decays mainly into the $U(1)_A$ channels $\eta\eta'$ and 4$\pi^0$. However, for a consistency of the whole approach, one needs broad-low mass gluonia (the $\sigma$ and its radial excitation), which couple strongly to the quark degrees of freedom similarly to the $\eta'$ of the $U(1)_A$ sector. Combining these results with the ones for the $\bar qq$ quarkonia, we present maximal quark-gluonium mixing schemes, which can provide quite a good description of the complex spectra and various decay widths of the observed scalar mesons $\sigma(1.0),f_0(0.98),f_0(1.37),f_0(1.5)$ and $f_J(1.71)$. In the tensor sector, the gluonium mass is found to be $M_T\simeq (2.05\pm 0.19)$ GeV, which makes the $\zeta(2.2)$ a good $2^{++}$ gluonium candidate, even though we expect a rich population of $2^{++}$ gluonia in this region. In the pseudoscalar channel, the gluonium mass is found to be $M_P\simeq (2.05\pm 0.19)$ GeV, while we also show that the $E/\iota(1.44)$ couples more weakly to the gluonic current than the $\eta'$, which can favour its interpretation as the first radial excitation of the $\eta'(0.96)$.