Masses, decays and mixings of gluonia in QCD

Abstract

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).

X(1835) as the lowest mass pseudoscalar glueball and proton spin problem

“…In the scalar sector of J P C = 0 ++ there are three candidates for the most low-lying mass glueball states as f 0 (1370), f 0 (1500) and f 0 (1710). Their masses are in fair agreement with the prediction of lattice QCD , m = 1.4 ∼ 1.8 GeV, [15] and also with QCD sum rules approaches [16,17]. However, for the pseudoscalar sector of (J P C = 0 −+ ), the situation is not so clear.…”

“…One should keep in mind that such correlations lead to the so-called topological charge screening effect, which is specially important for flavor singlet pseudoscalar channel (see discussion in [3] and [17]). It would not be worthless to point out that the mass of X(1835) is quite close to the lowest value predicted by QCD sum rules for pseudoscalar glueball M P = 1.86 GeV [16] and M P = 2 GeV [17]. Now we are in position to estimate the coupling of X(1835) with gluons.…”

“…Only η(1440) is being discussed as a possible candidate for the pseudoscalar glueball [18,19]. But, this identification is doubted by large disagreement between its experimental observation and theoretical predictions of both lattice QCD [15] and QCD sum rules calculation [16,17], of which values range between m = 1.86 and 2.7 GeV. Furthermore, the peculiarities of η(1440) production in different reactions support these doubts on its glueball origin [20,21].…”

Quark Effects in the Gluon Condensate Contribution to the Scalar Glueball Correlation Function

“…The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contribution to those QCD sum-rules independent of the low-energy theorem (the subtracted sum-rules).The QCD correlation function of scalar gluonic currentsis used to study the properties of scalar gluonium via QCD sum-rule techniques [1,2]. The current J(x) is the lowest-order version of the operator β(α)G 2 (x), which is renormalization-group invariant for chiral quarks [3,4].…”

Topological charge screening and pseudoscalar glueballs

“…One such opportunity was recently exploited in OCD sum rule analyses, which found nonperturbative short-distance physics in the form of direct instantons [2] to play a crucial role in the structure and dynamics of the scalar (0 ++ ) glueball [3,4]. Indeed, the instanton-improved operator product expansion (IOPE) of the 0 ++ glueball correlator resolves two longstanding problems of the conventional sum rules (the mutual inconsistency of different Borel moment sum rules and the conflict with the underlying low-energy theorem [5,6]), generates new scaling relations between fundamental glueball and instanton properties, and leads to improved sum rule predictions for scalar glueball properties [3]. (See also the subsequent gaussian sum rule analysis [7], based on the same instanton contributions.)…”