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.

Figure 1

Momenta of particles in the $K^{+}\gamma \to K^{+}{\pi }^0$ reaction.

Figure 2

Attaching photon to the quark propagators, we get box diagrams describing anomaly contributions to (a) the $K^{+}\gamma \to K^{+}{\pi }^0$, (b) $K^{+}\gamma \to K^0{\pi }^{+}$, and (c),(d) ${\pi }^{+}\gamma \to {\pi }^{+}{\pi }^0$ reactions.

Figure 3

Vector meson exchanges in the process $K^{+}\gamma \to K^{+}{\pi }^0$: $K^{*+}$ meson in (a) $s$ and (b) $u$ channels, and (c) ${\rho }^0$, $\omega$, $\varphi$ mesons in the $t$ channel.

Figure 4

Vector meson exchanges in the process $K^{+}\gamma \to K^0{\pi }^{+}$: (a) $K^{*+}$ in the $s$ channel, (b) $K^{*0}$ in the $u$ channel, (c) ${{\rho }^{+}}^{}$ in the $t$ channel.

Figure 5

Differential cross sections of the reactions $K^{+}N\to K^{+}{\pi }^{0}N$ and $K^{+}N\to K^0{\pi }^{+}N$ for $N={}^{63}\mathrm{Cu}$. The two solid lines for the $K^{+}N\to K^{+}{\pi }^{0}N$ reaction correspond to the two possible choices of the signs of the product of coupling constants (see Appendix pp2).

Figure 6

Differential cross sections of the reaction $K^{+}N\to K^{+}{\pi }^{0}N$ for $N={}^{63}\mathrm{Cu}$. The two solid lines correspond to the two possible choices of the signs of the product of coupling constants.

Figure 7

Kinematics of the $K^{+}\gamma \to K^{+}{\pi }^0$ reaction in the center of mass system. Initial particles are moving along the $z$ axis.

Figure 8

Diagrams used for the calculation of vector meson coupling constants. (a) $f_{K^{*+}{K}^{+}{\pi }^0}$, (b) $f_{K^{*+}{K}^{+}\gamma }$