nique and reviews of its methodology are given in Refs. [104, 38, 89]. QSR depends critically on the concept of quark-hadron duality, which asserts that hadrons can be described equally well in terms resonances or in terms of bound states composed of quarks and gluons. This du- ality is realized globally rather than locally, in the sense that the two descriptions agree when suitably averaged. Calculations on the QCD side of the duality relation can be performed using the OPE, which naturally includes both perturbative and non-perturbative effects. The hadron side of the duality can be invoked using an experimentally known hadronic spec- tral function, or a suitable resonance model. Ultimately there are two main applications of QSR that utilize this duality in opposite directions. The first uses experimentally known hadronic parameters to determine unknown QCD parameters, such as quark masses (see e.g. Ref. [91]). The second involves determining unknown hadronic parameters in terms of known QCD parameters, using an appropriate model for the hadronic spectral function. The research presented in Chapters 3, 4 and 6 uses the second approach to predict the properties of exotic hadrons. All QSR calculations begin with a QCD correlation function of the form where the current J is a composite operator that couples to the hadron being studied. Tech- niques for calculating the correlation function will be discussed in Section 1.4.3. The analytic properties of the correlation function (1.71) can be used to show that Π ( Q $^{2}$) and its imag- inary part ImΠ ( Q $^{2}$) are related by a dispersion relation. In turn, ImΠ ( Q $^{2}$) is related to a hadronic spectral function. Quark-hadron duality is therefore encoded through this disper- sion relation. We will now demonstrate how the dispersion relation can be derived by appealing to the analytic properties of the correlation function. To do so, we will calculate the contour integral I = ∮ C dz 2 πi Π ( z ) z $^{n}$( z − Q $^{2}$) , (1.72) Π $^{(}$Q 2 ) = i$^{∫}$ d $^{4}$x e iq · x 〈 Ω | [ J ( x ) J $^{†}$(0) ] | Ω 〉 , Q 2 = − q $^{2}$, (1.71) 1.4.1 Dispersion Relation 34