Looking for chiral anomaly in $K \gamma \to K \pi$ reactions

In an experiment currently being performed at the Institute for High Energy Physics, Serpukhov, Russia, a beam of charged kaons is directed on a copper target. In the electromagnetic field of the target nuclei, two reactions occur: $K^+ \gamma \to K^+ \pi^0$ and $K^+ \gamma \to K^0 \pi^+$. A peculiar distinction between these two reactions is that there is a chiral anomaly contribution in the former reaction, but not in the latter. This contribution can be directly seen through comparison of the cross sections of these reactions near the threshold. We derive expressions for these cross sections taking into account the anomaly and the contribution of the lightest vector mesons.