an infinite number of distinct QCD vacua, whom differ from one another by their topological equivalence class: π$_{3}$ ( S $^{3}$) = Z . Furthermore, it can be shown that whenever a correlation function tunnels in and back out of a vacuum in a different topological class, it picks up a contribution to the axial symmetry: where Q is defined as the topological charge, and can be shown to be equal to the number of left handed fermions minus the number of right handed fermions: Q = n$_{L}$ − n$_{R}$ . An instanton is defined as those solutions for which Q = 1. Probably the simplest way to think of instantons is as isolated sources of axial symmetry breaking, and they are responsible for making the η ′ (958) meson heavy. More detailed analysis can be found in the sources quoted earlier. Now that we’ve investigated some of the complex features of QCD, a pru- dent question would be to ask whether we have the theoretical tools required to calculate experimental quantities such as hadron masses and decay con- stants. These are very difficult quantities to determine. Current approaches can be divided into four classifications. Feynman diagrams are used highly successfully in QED to calculate cross-sections. The correlation function is expanded in terms of a small parameter, α ≈ 1 / 137, and then each contribution is calculated order-by-order. Beyond one loop the calculations can get very in- 24 1.3 Solving QCD Q = − 1 2 n$_{f}$ ∫ ∂$_{µ}$j µ 5 (1.41) • Perturbative QCD