Calculation of the anomalous γπ ∗ → ππ form factor

The form factor for the anomalous process γπ ^∗ → ππ , F^{3 π}( s, t, u), is calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The chiral-limit value dictated by the electromagnetic, anomalous chiral Ward identity, is reproduced, independent of the details of the modelling of the gluon and quark 2-point Schwinger functions. Using a parametrization of the dressed u- d quark 2-point Schwinger function that provides a good description of pion observables F^{3 π}( s, t, u) is calculated on a kinematic range that proposed experiments plan to explore. Our result confirms the general trend of other calculations, i.e., a monotonic increase with s at fixed t and u, but is uniformly larger and exhibits a more rapid rise with s.