operator product expansion (OPE) [127]: where the Wilson coefficients C$_{n}$ ( x ) are functions of x and : O$_{n}$ (0) : are normal ordered composite operators of dimension n (the dimensions of quark and gluon fields are discussed in Appendix A). Taking the vacuum expectation value and moving to momentum space, the OPE reads The lowest dimensional operator in the OPE is the identity operator, which corresponds to purely perturbative contributions. Each higher dimensional operator O$_{n}$ (0) is a normal ordered combination of quark and gluon fields whose vacuum expectation value does not van- ish. These are called condensates and represent non-trivial features of the QCD vacuum | Ω 〉 . Through the OPE, QSR analyses naturally include both perturbative and non-perturbative effects. The OPE involves an implicit separation of scales: the condensates and Wilson coefficients represent low and high energy phenomena, respectively. As such, the Wilson co- efficients can be calculated perturbatively. The condensates are gauge invariant and Lorentz invariant combinations of quark and gluon fields. The two most important condensates are the quark and gluon condensates both of which have dimension four. Note that the quark condensate does not include heavy flavours because the heavy quark condensate can be related to the gluon condensate. It is important to stress that the numerical values of condensates cannot be calculated directly within QCD. Rather, they must be determined empirically. One such method involves using QSR duality relations to relate condensates to experimental data, for instance. The quark condensate can be defined in terms of the pion mass and decay constant via the Gell-Mann- 42 m$_{q}$ 〈 ¯ qq 〉 = m$_{q}$ 〈 Ω | : ¯ q (0) q (0) : | Ω 〉 , α 〈 G $^{2}$〉 = α 〈 Ω | : G a µν (0) G µν a (0) : | Ω 〉 , (1.100) lim Q $^{2}$→∞ ∫ d $^{4}$x e iq · $^{x}$J ( x ) J $^{†}$(0) = ∑ n 〈 Ω | : O$_{n}$ (0) : | Ω 〉 ∫ d $^{4}$x e iq · $^{x}$C$_{n}$ ( x ) . (1.99) lim x → $_{0}$J ( x ) J $^{†}$(0) = ∑ n C$_{n}$ ( x ) : O$_{n}$ (0) : , (1.98)