Harnett, DerekSteele, Tom2020-08-052020-08-052020-072020-08-05July 2020http://hdl.handle.net/10388/12947In this thesis, we examine three papers that my coauthors and I have published. The overarching theme of this work will be the use of QCD Laplace sum rules applied to quarkonium or quarkonium-like systems containing heavy quarks in an attempt to explore ideas relating to beyond-the-quark-model hadrons, including hybrids (mesons with gluonic content) and multi-quark meson-like states. In the first two papers [1, 2], we study mixing between conventional mesons and hybrids in vector and axial vector charmonium-like and bottomonium-like systems. We compute meson-hybrid cross-correlators within the operator product expansion, including condensate contributions up to dimension-six. We then use the measured masses of heavy quarkoniumlike states as inputs into a QCD Laplace sum-rules calculation to probe known resonances for nonzero coupling to both the conventional meson and hybrid currents. Nonzero coupling to both of these currents would signal meson-hybrid mixing. We find nonzero mixing in a number of resonances over all four of the mass spectra which we probed. The results from both [1] and [2] are collected and discusses in section 2.7. In the third paper [3], constituent mass predictions for axial vector cc and bb diquarks are generated using QCD Laplace sum-rule methods. We calculate the diquark correlator within the operator product expansion to next-to-leading-order, including condensate contributions up to dimension-six. We find that the constituent mass of the cc diquark is (3.51 ± 0.35) GeV and the constituent mass of the bb diquark is (8.67 ± 0.69) GeV. We then use these diquark constituent masses as inputs to calculate several tetraquark masses within the Type-II chromomagnetic interaction diquark-antidiquark tetraquark model. The results from the calculations done in [3] are collected in section 3.3.application/pdfMesonHybridMixingDiquarkTetraquarkQCDSum RulesThesis2020-08-05