The U(1) Anomalous Ward Identities and Chiral Dynamics

It is generally believed that the QCD Lagrangian has N^{2}_{f} conserved axial currents except for quark mass terms. In the world of zero bare quark masses for the first L flavours, the corresponding conservation laws are spontaneously broken and L² pseudo-Goldstone bosons are thought to be generated. For three quark flavours the absence of the ninth light pseudoscalar in the real world is a well-known puzzle first pointed out by Glashow^[1] and studied subsequently by Wienberg^[2] Kogut and Susskind^[3] and many others^[4-8]…