QSR calculations. Table 1.4 summarizes the research presented in subsequent chapters. Table 1.4: Summary of thesis research. 51 Chapter Description and Key Results Themes 1 2 3 3 QSR study of J PC = 1 $^{++}$, 0 − + heavy quarkonium hybrids. ✓ ✓ M (1 $^{++}$, c ¯ cg ) = 5 . 13 ± 0 . 25 GeV, M (0 − $^{+}$, c ¯ cg ) = 3 . 82 ± 0 . 13 GeV. These results preclude the pure charmonium hybrid interpretation of the X (3872) and support the charmonium hybrid interpretation of the Y (3940). 4 QSR study of J PC = 0 $^{±}$, 1 ± heavy-light diquarks. ✓ ✓ ✓ M (0 $^{+}$, cq ) = 1 . 86 ± 0 . 05 GeV, M (1 $^{+}$, cq ) = 1 . 87 ± 0 . 10 GeV, M (0 $^{+}$, bq ) = M (1 $^{+}$, bq ) = 5 . 20 ± 0 . 10 GeV. These masses are consistent with constituent diquark models, providing QCD-based support for the tetraquark interpretation of the X (3872), Z ± c (3895), Y$_{b}$ (10890), Z ± b (10610) and Z ± b (10650). The renormalization methodology needed for next-to-leading order QSR calculations is also developed. 5 Calculation of two-loop scalar diquark operator renormalization factor. ✓ ✓ The renormalization factor and anomalous dimension are calculated to O ( α $^{2}$). These results are utilized in Chapter 4. 6 QSR analysis of mixing between scalar gluonium and quark mesons. ✓ ✓ The perturbative contribution to the non-diagonal scalar gluonium-quark meson correlation function is calculated. The renormalization methodology needed for QSR studies involving non-diagonal correlation functions is developed.