The number of colors in the decays ${\pi^0, \eta, \eta' \rightarrow \gamma\gamma}$

Abstract.

The decays $\pi^0, \eta, \eta' \rightarrow \gamma \gamma$ are investigated up to next-to-next-to-leading order in the framework of the combined 1/N _c and chiral expansions. Without mixing of the pseudoscalar mesons the N _c independence of the $\pi^0$ and $\eta$ decay amplitudes is shown to persist at the one-loop level, although the contribution of the Wess-Zumino-Witten term to the pertinent vertices is not canceled by the N _c dependent part of a Goldstone-Wilczek term. The decay amplitude of the singlet field, on the other hand, depends strongly on N _c and yields under the inclusion of mixing also a strong N _c dependence for the $\eta$ decay. Both the $\eta$ and $\eta'$ decay are suited to confirm the number of colors to be N _c = 3.