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Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomoniumhybrids are determined using QCD Laplace sum-rules. The effects of thedimension-six gluon condensate are included in our analysis and result in astable sum-rule analysis, whereas previous studies of these states were unableto optimize mass predictions. The pseudoscalar charmonium hybrid is predictedto have a mass of approximately 3.8 GeV and the corresponding bottomoniumprediction is 10.6 GeV. Calculating the full correlation function, rather thanonly the imaginary part, is shown to be necessary for accurate formulation ofthe sum-rules. The charmonium hybrid mass prediction is discussed within thecontext of the X Y Z resonances.

Mass Predictions for Pseudoscalar $J^{PC}=0^{-+}$ Charmonium and Bottomonium Hybrids in QCD Sum-Rules