Decay π⁰→γγ to next to leading order in chiral perturbation theory

The π⁰→γγ decay width is analyzed within the combined framework of chiral perturbation theory and the 1/N_c expansion up to O(p⁶) and O(p⁴×1/N_c) in the decay amplitude. The η^′ is explicitly included in the analysis. It is found that the decay width is enhanced by about 4.5% due to the isospin-breaking induced mixing of the pure U(3) states. This effect, which is of leading order in low energy expansion, is shown to persist nearly unchanged at next to leading order. The chief prediction with its estimated uncertainty is Γ_π⁰→γγ=8.10±0.08eV. This prediction at the 1% level makes the upcoming precision measurement of the decay width even more urgent. Observations on the η and η^′ can also be made, especially about their mixing, which is shown to be significantly affected by next to leading order corrections.