We compute the masses and decay widths of the 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 ± 0.2) GeV, which decays mainly into the U (1) A channels ηη ′ and 4π 0 . However, for a consistency of the whole approach, one needs broad-low mass gluonia (the σ B and its radial excitation), which couple strongly to the quark degrees of freedom similarly to the η ′ of the U (1) A sector. Combining these results with the ones for theqq quarkonia, we present maximal gluonium-quarkonium mixing schemes, which can provide quite a good description of the complex spectra and various decay widths of the observed scalar mesons σ(1.), 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 ≃ (2.0 ± 0.1) GeV, which makes the ζ(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 ≃ (2.05 ± 0.19) GeV, while we also show that the E/ι(1.44) couples more weakly to the gluonic current than the η ′ (0.96), which can favour its interpretation as the first radial excitation of the η ′ (0.96).
We consider the assumption that a tachyonic gluon mass imitates short-distance nonperturbative physics of QCD. The phenomenological implications include modifications of the QCD sum rules for correlators of currents with various quantum numbers. The new 1/Q 2 terms allow to resolve in a natural way old puzzles in the pion and scalar-gluonium channels. They lead to a slight reduction of the values of the running light quark masses from the (pseudo)scalar sum rules and of αs(Mτ ) from τ decay data. Analogously such terms only affect slightly the determinations of the running strange quark mass from e + e − and τ decay data. Further tests can be provided by precision measurements of the correlators on the lattice and by the e + e − → hadrons data.
We use QCD spectral sum rules to test the nature of the meson X(3872), assumed to be an exotic four-quark (ccqq) state with J P C = 1 ++ . For definiteness, we work with the current proposed recently by Maiani et al [1], at leading order in αs, consider the contributions of higher dimension condensates and keep terms which are linear in the light quark mass mq. We find MX = (3925±127) MeV which is compatible, within the errors, with the experimental candidate X(3872), while the SU(3) breaking-terms lead to an unusual mass-splitting MXs − MX = −(61 ± 30) MeV. The massdifference between the neutral states due to isospin violation of about (2.6 ∼ 3.9) MeV is smaller than the value (8±3) MeV proposed in [1]. For the b-quark, we predict MX b = (10144±106) MeV for the X b (bbqq), which is much below theBB * threshold in contrast to theBB * molecule prediction [2], and for the X s b (bbss), a mass-splitting M X s b − MX b = −(121 ± 182) MeV. Our analysis also indicates that the mass-splitting between the ground state and the radial excitation of about (225 ∼ 250) MeV is much smaller than in the case of ordinary mesons and is (within the errors) flavour-independent. We also extract the decay constants, analogous to fπ, of such mesons, which are useful for further studies of their leptonic and hadronic decay widths. The uncertainties of our estimates are mainly due to the ones from the c and b quark masses.
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