calculated explicitly. Specifically, Π$_{GGG}$ ( Q $^{2}$) is singular at the hadronic threshold t$_{0}$ = 4 m $^{2}$. This singularity also appears in the imaginary part ImΠ$_{GGG}$ ( Q $^{2}$), and hence when the sum rules are formulated the integration in Eq. (1.95) is singular at the lower limit. This difficulty can be overcome by noting that Laplace sum rules (1.86) involve the inverse Laplace trans- form of the entire correlation function. The inverse Laplace transform can be calculated via a limiting procedure so that the sum rules are well defined at the hadronic threshold. How- ever, the imaginary part of the correlation function alone is insufficient to do this. Therefore the the entire correlation function must be calculated explicitly, and the loop integration techniques discussed in Chapter 2 are indispensable for this. 3.3 Published Articles • D. Harnett, R.T. Kleiv, T.G. Steele, and Hong-Ying Jin, Axial Vector J PC = 1 ++ Char- monium and Bottomonium Hybrid Mass Predictions with QCD Sum-Rules, J. Phys. G39 (2012) 125003, arXiv:1206.6776 [hep-ph]. • R. Berg, D. Harnett, R.T. Kleiv, and T.G. Steele, Mass Predictions for Pseudoscalar J PC = 0 − + Charmonium and Bottomonium Hybrids in QCD Sum-Rules, Phys. Rev. D86 (2012) 034002, arXiv:1204.0049 [hep-ph]. The J PC = 1 ++ heavy quarkonium hybrid paper was published in the Journal of Physics G in 2012, while the J PC = 0 − + heavy quarkonium hybrid paper was published in Physical Review D in 2012. Links to the published journal articles and preprints are included below for each paper. 81