Anomalies and the WZW term of two-flavor QCD

The $\mathrm{U}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}{\mathrm{}\left(2\right)\mathrm{}}_L$ symmetry of QCD with two massless flavors is subject to anomalies which affect correlation functions involving the singlet currents $A_{\mu }^0$ or $V_{\mu }^0.$ These are relevant for $\pi \gamma$ interactions, because—for two flavors—the electromagnetic current contains a singlet piece. We give the effective Lagrangian required for the corresponding low energy analysis to next-to-leading order, without invoking an expansion in the mass of the strange quark. In particular, the Wess-Zumino-Witten term that accounts for the two-flavor anomalies within the effective theory is written down in closed form.