Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next-lowest weighted sum-rules. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance model does not provide an adequate description of the hadronic spectral function. Consequently, we consider a wide variety of phenomenological models which distribute resonance strength over a broad region-some of which lead to excellent agreement between the theoretical prediction and phenomenological models. Including QCD uncertainties, our results indicate that the hadronic contributions to the spectral function stem from a pair of resonances with masses in the range 0.8-1.6 GeV, with the lighter of the two potentially having a large width.

We have extended the calculation of the correlation functions of heavy quarkonium hybrid operators with various J P C quantum numbers to include QCD condensates up to dimension six. In contrast to previous analyses which were unable to optimize the QCD sum-rules for certain J P C , recent work has shown that inclusion of dimension six condensates stabilizes the hybrid sum-rules and permits reliable mass predictions. In this work we have investigated the effects of the dimension six condensates on the remaining channels. After performing the QCD sum-rule analysis, we update the mass spectra of charmonium and bottomonium hybrids with exotic and non-exotic quantum numbers. We identify that the negative-parity states with J P C = (0, 1, 2) −+ , 1 −− form the lightest hybrid supermultiplet while the positive-parity states with J P C = (0, 1) +− , (0, 1, 2) ++ belong to a heavier hybrid supermultiplet, confirming the supermultiplet structure found in other approaches. The hybrid with J P C = 0 −− has a much higher mass which may suggest a different excitation of the gluonic field compared to other channels. In agreement with previous results, we find that the J P C = 1 ++ charmonium hybrid is substantially heavier than the X(3872), which seems to preclude a pure charmonium hybrid interpretation for this state.

Masses of the pseudoscalar (J PC ¼ 0 Àþ ) charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeVand the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulation of the sum-rules. The charmonium hybrid mass prediction is discussed within the context of the XYZ resonances.

Techniques for using Gaussian QCD sum-rules to predict hadronic resonance properties are developed for single-resonance and two-resonance phenomenological models, and criteria are developed for determining which of these models is required for analyzing a particular hadronic channel. The vector current sum-rule coupled to the ρ meson is shown to be consistent with a single resonance model, and the Gaussian sum-rule analysis results in an accurate ρ mass prediction which exhibits excellent agreement between the theoretical prediction of the Gaussian sum-rule and the phenomenological model. A two-resonance model is shown to be necessary for the Gaussian sum-rule for the non-strange quark scalar (nn) currents. The two-resonance Gaussian sum-rule analysis of the isoscalar and isovector (I = 0, 1)nn scalar mesons exhibits excellent agreement between the theoretical prediction and phenomenological model. The prediction of the resonance properties of the I = 0, 1 nn scalar mesons in this two-resonance model provides valuable information for the interpretation of the scalar mesons, including the X(1775).

Axial vector (J P C = 1 ++ ) charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for 1 −− and 0 −+ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result for the charmonium-like "XYZ" states and the charmonium hybrid multiplet structure observed in recent lattice calculations.