The number of colors in the decays

B. Borasoy

doi:10.1140/epjc/s2004-01713-9

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2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C (2004) 34: 317-326
https://doi.org/10.1140/epjc/s2004-01713-9

theoretical physics

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

B. Borasoy^*

Physik Department, Technische Universität München, 85747, Garching, Germany

^* e-mail: borasoy@ph.tum.de

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.