Chapter 7 Conclusions Heavy quarkonium spectroscopy is a rapidly changing field, both experimentally and theoretically. In recent years many heavy quarkonium-like states have been discovered by the Babar, Belle, BES-III, CDF, CLEO, D0, and LHCb experiments. It is entirely possible that more heavy quarkonium-like states will be discovered by these experiments, or by new experiments being planned such as Belle-II [15] and PANDA [83]. The heavy quarkonium sector provides perhaps the most promising “hunting ground” for exotic hadrons. Firm theoretical predictions for the properties of exotic hadrons are needed in order to determine the true nature of the heavy quarkonium-like states. The main theme of research presented in this thesis has been to utilize QSR techniques to determine mass predictions for exotic hadrons that could exist among the heavy quarkonium- like states. This work has direct implications for the XYZ states. In Chapter 3 the mass of the J PC = 0 − + charmonium hybrid was found to be 3 . 82 ± 0 . 13 GeV, which is compatible with the Y (3940). In Ref. [5] it was suggested that this particle could be a charmonium hybrid, and the mass prediction extracted in Chapter 3 is compatible with this interpretation. More experimental work is needed to establish the J PC quantum numbers of this state. Similarly, the 1 ++ charmonium hybrid mass was predicted to be 5 . 13 ± 0 . 25 GeV in Chapter 3. The LHCb collaboration has confirmed that the X (3872) has J PC = 1 ++ [2], therefore the mass prediction in Chapter 3 helps to rule out the pure charmonium hybrid interpretation of this state [77]. In Chapter 4 the J P = 0 + and 1 + charm-light diquark masses were predicted to be 1 . 86 ± 0 . 05 GeV and 1 . 87 ± 0 . 10 GeV. In Ref. [84] the X (3872) was interpreted as a tetraquark using a constituent diquark model. The J P = 0 + and 1 + charm-light diquark masses were determined to be 1 . 93 GeV, which is compatible with the mass predictions extracted in Chapter 4. This agreement provides QCD support for the predictions of the 95