The number of colors in the decays pi^0, eta, eta-prime -> gamma gamma

Abstract

The decays pi^0, eta, eta-prime -> 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-prime decay are suited to confirm the number of colors to be N_c=3.