Chiral Loops in ${\pi }^0$, ${\eta }^0\to \gamma \gamma$ and $\eta -{\eta }^{\prime }$ Mixing

We compute the one-loop corrections to the Wess-Zumino Lagrangean governing ${\pi }^0$, ${\eta }_8\to \gamma \gamma$. The SU(3) relation between the two decay rates receives modifications of order $m_K^2\ln m_K^2$, as does the Gell-Mann-Okubo mass formula. A consistent picture of $\eta -{\eta }^{\prime }$ mixing emerges from both the two-photon widths and the mass matrix, however with a mixing angle $\theta \approx -20\mathrm{}°$ instead of the usual $\theta \approx -10\mathrm{}°$.