constituent diquark model developed in Ref. [84]. In particular, this agreement provides indirect support for the tetraquark interpretation of the Z ± c (3895). The J P = 0 + and 1 + bottom-light diquark masses were also extracted in Chapter 4, finding a common mass of 5 . 08 ± 0 . 04 GeV. This is in reasonable agreement with the constituent bottom-light diquark mass of 5 . 20 GeV determined from a constituent diquark model of the Y$_{b}$ (10890) in Ref. [10]. Therefore the bottom-light diquark mass prediction extracted in Chapter 4 supports the tetraquark interpretations of the Y$_{b}$ (10890), Z ± b (10610) and Z ± b (10650). A secondary theme in this research has been renormalization methodology. QSR cal- culations involve correlation functions of composite local operators. The renormalization of these composite operators can significantly complicate QSR calculations. In Chapter 4, next-to-leading order perturbative contributions to the heavy-light diquark correlation func- tion were calculated. In order to renormalize these contributions the heavy quark mass and diquark current must be renormalized. The scalar diquark operator renormalization factor was determined in Chapter 5. A QSR analysis of mixing between scalar mesons and gluo- nium was performed in Chapter 6. The leading order perturbative contribution to the bare non-diagonal correlation function was found to contain a non-local divergence. This problem was resolved through the use of the renormalized scalar glueball operator, which mixes under renormalization with the scalar meson operator. The renormalization induced contributions of the scalar meson operator served to cancel the divergence in the bare non-diagonal corre- lation function. The research in Chapters 4 and 6 illustrates the two distinct ways in which composite operator renormalization can complicate QSR calculations: it can be required in leading order contributions due to operator mixing or in higher order contributions due to the multiplicative renormalization of the current being used. The QSR calculations in this thesis have largely been concerned with heavy quarkonium- like states that contain heavy quarks. Unlike calculations that involve only light quarks whose masses can be neglected, the heavy quark mass cannot be ignored. In practice this means that loop integrals that involve heavy quarks are much more complicated than those that involve only light quarks. The loop integration techniques developed in Chapter 2 are crucial to the QSR analyses in Chapters 3 and 4. In addition, the renormalization methodology used in Chapters 4 and 6 is dependent upon the loop integration methods discussed in Chapter 2. 96