cussed in Chapter 1, the X (3872) is most often interpreted as a four-quark state. There has also been an attempt to describe it as a charmonium hybrid [77]. However, the hybrid interpretation has been largely set aside due to the fact that several different theoretical approaches predict an axial vector charmonium hybrid mass that is much greater than that of the X (3872) [17, 99, 79, 78]. With the mass predictions that we have extracted, QSR is now in agreement with these other theoretical approaches. Therefore this work has helped to rule out the pure charmonium hybrid interpretation of the X (3872). However, it should be noted that the results of this work cannot exclude the possibility that the X (3872) could be a mixture of various hadronic structures, perhaps with a hybrid component. The latter possibility is explored in Ref. [32]. The pseudoscalar channel sum rule analysis lead to mass predictions of 3 . 82 ± 0 . 13 GeV and 10 . 64 ± 0 . 19 GeV for the charmonium and bottomonium hybrids, respectively. Both of these mass predictions are significantly lower than the mass predictions of the original studies of Govaerts et al. which were derived from unstable sum rules. Similar to the recent work in the vector channel, inclusion of the dimension-six gluon condensate was found to stabilize the pseudoscalar channel sum rules. Including the theoretical uncertainty, the pseudoscalar charmonium hybrid mass prediction is comparable to the mass of the Y (3940) [5, 14]. This particle has been identified as a charmonium hybrid candidate [5], and our mass prediction supports this claim. However, to date the quantum numbers of this state have not yet been firmly established. More experimental work is needed to determine the true nature of the Y (3940). The research in this chapter contributes to several of the themes of this thesis. First, the heavy quarkonium hybrid mass predictions presented here will help to unravel the true nature of the enigmatic heavy quarkonium-like states. It is also interesting to note that the vector [102], axial vector [60] and pseudoscalar [19] charmonium hybrid mass predic- tions derived from QSR are in qualitative agreement with the charmonium hybrid multiplet structure predicted using lattice QCD [78]. Second, the calculations of the axial vector and pseudoscalar heavy quarkonium hybrid correlation functions profitably apply the loop inte- gration techniques discussed in Chapter 2. In order to properly formulate the contributions of the dimension-six gluon condensate to the sum rules the entire correlation function must be 80