Isospin violating effects, both due to the nonvanishing quark mass difference $m_d-m_u$ and to virtual photons, are studied by fitting the squared masses of pseudoscalar mesons to the next-to-leading order in the simultaneous expansion in powers of $1/N_c$, momenta, and quark masses. It is shown that electromagnetic corrections significantly affect the values of the ${\pi }^0-\eta$ and ${\pi }^0-{\eta }^{\prime }$ mixing angles and have virtually no effect on the $\eta -{\eta }^{\prime }$ mixing angle. The ${\pi }^0,\eta ,{\eta }^{\prime }\to \gamma \gamma$ decay widths are calculated. In particular, it is found that ${\mathrm{\Gamma }}_{{\pi }^0\to \gamma \gamma }=7.82\pm 0.01\mathrm{eV}$. This result is in full agreement with the latest data of the PrimEx-I and PrimEx-II collaborations ${\mathrm{\Gamma }}_{{\pi }^0\to \gamma \gamma }^{\exp }=7.802\pm 0.052(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}.)\pm 0.105(\mathrm{syst}.)\mathrm{eV}$.

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• Anomalies
• Effective field theory
• Large-N expansion in field theory
• Particle decays
• Particle interactions
• Particle mixing & oscillations
• Strong interaction