Four-photon decay of the neutral pion

The decay rate for π⁰→4γ is estimated to order α⁴ in several models and found to be considerably suppressed by the angular momentum barriers required by gauge invariance and even further suppressed in models satisfying a partially-conserved-axial-vector-current condition. Typical values for $\frac{\Gamma ({\pi }^0\to 4\gamma )}{\Gamma ({\pi }^0\to 2\gamma )}$ range from 4 × 10⁻¹⁴ to 10⁻¹⁶. We conclude that the dominant contribution is likely to come from an electron-loop diagram contributing in order α⁶ but without angular momentum barriers.