into one another through Fierz transformations. In Ref. [129] it was pointed out that this ambiguity obscures the nature of the hadronic states that are probed by these currents. For this reason QSR studies that utilize currents containing four quark fields cannot distinguish between the molecular and tetraquark scenarios. An alternative approach to studying four-quark states within QSR is to use diquark cur- rents. Using QSR the diquark mass can be calculated and can be thought of as a constituent diquark mass. This in turn can be used in constituent diquark models of tetraquarks. This approach was first used in Ref. [129] to study tetraquarks composed of light quarks. There are several benefits to this approach for studying four-quark states in QSR. First, it avoids the Fierz transformation ambiguities associated with four-quark currents. This is perhaps the only way that pure tetraquark states can be studied using QSR. Second, the composite operators in Eq. (4.1) mix under renormalization [92, 65]. For this reason it is challenging to extend QSR studies using four-quark currents to higher orders. However, as discussed in Chapter 1, the diquark current does not mix with other operators under renormalization. The renormalization factor of the scalar ( J P = 0 $^{+}$) diquark operator is determined to two- loop order in Ref. [70] and is the subject of Chapter 5. For these reasons QSR studies using diquark currents can be extended to higher order in the perturbative expansion much more easily than those that use four-quark currents. In Ref. [84] the X (3872) is interpreted as a tetraquark using a constituent diquark model where the scalar (0 $^{+}$) and axial vector (1$^{+}$) charm-light diquark masses are assumed to be degenerate due to heavy quark symmetry. The constituent charm-light diquark mass is determined to be 1 . 93 GeV from a fit to the X (3872). The model also predicts the existence of electrically charged tetraquarks that are members of the same nonet as the X (3872). The recently discovered Z ± c (3895) appears to be compatible with this prediction [48]. A similar analysis was performed in Ref. [10] where a bottom-light constituent diquark mass of 5 . 20 GeV was extracted from a fit to the tetraquark candidate Y$_{b}$ (10890) [31]. The results of the analysis support the tetraquark interpretation of the charged bottomonium-like states Z ± b (10610) and Z ± b (10650) which were discovered by the Belle collaboration [26]. Essential features of these constituent diquark models are that the masses of the scalar (0 $^{+}$) and axial vector (1 $^{+}$) diquarks are assumed to be identical, and that the constituent diquark masses 83