to be the minimum value s min 0 . The optimal value of s$_{0}$ is determined using The optimal value of s$_{0}$ is that which minimizes (1.115). The sum in Eq. (1.115) is calculated over the sum rule window corresponding to s min 0 . Once the optimal value s opt 0 has been determined, the mass can be extracted by fitting M $^{(}$s opt 0 , τ ) to a constant over the sum rule window. The QSR method has been applied to a wide variety of problems in hadronic physics. In particular, QSR calculations provide crucial information on the properties of exotic hadrons. This theoretical input helps to guide the experimental search for such states. The majority of QSR studies of exotic hadrons have focused on those that are much lighter than the heavy quarkonium-like states (see Ref. [89] for a detailed review). However, the recently discovered XYZ states have motivated QSR studies of exotic hadrons that may exist within the same mass region as heavy quarkonia. Nearly all of this work has considered four-quark states, which can be realized as molecules or tetraquarks (Ref. [94] provides a review). A common feature of all of these studies is the use of currents that contain four quark fields. However, for reasons discussed in Chapter 4, QSR studies that use four-quark currents cannot distinguish between the molecular and tetraquark configura- tions. An alternate approach is to use diquark currents, which are relevant to tetraquarks only. This approach was first applied to diquarks containing a heavy quark in Ref. [125]. The research presented in Chapter 4 serves to extend this work. Hybrid mesons could also exist in the heavy quarkonium mass region. Surprisingly, this possibility has been little explored by QSR practitioners. Refs. [55, 56, 54] comprise the earliest QSR studies of heavy quarkonium hybrids. These studies examined a wide variety of J PC channels. However, the sum rules for many channels exhibited instabilities, and hence the resulting mass predictions in those channels are unreliable. Ref. [102] recently performed 49 1.4.5 QCD sum rules and Heavy Quarkonium-like states χ $^{2}$( s$_{0}$ ) = ∑ j ( 1 M$^{√}$ R$_{1}$ ( τ$_{j}$, s$_{0}$ ) R$_{0}$ ( τ$_{j}$, s$_{0}$ ) − 1$^{)}$$^{2}$ , s$_{0}$ ≥ s min 0 . (1.115)