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 $\eta {\eta }^{\prime }$ 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 ${\eta }^{\prime }$ of the $U(1{)}_A$ sector. Combining these results with the ones for the $\bar{q}q$ 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 ${\eta }^{\prime }$, which can favour its interpretation as the first radial excitation of the ${\eta }^{\prime }(0.96)$.

Comments: 33 pages, latex 2e source+19 figures inside the text, compressed files, minor changes (version to appear in Nucl.Phys. B) Montpellier preprint PM 96/37