Theorems and bounds relating to the two-photon decay of the pion

An exact bound on the π⁰→2γ vertex function is derived. Form it, it is possible to estimate bounds to the corrections to the vector-dominance model, the anomalous constant S, and the asymptotic behavior of the form factor. A theorem is derived which states that, under specific assumptions, the coefficient (K) of the axial current in the short-distance expansion of two electromagnetic currents is finite if ${\sigma }_{e^{+}{e}^{-}}\to \frac{1}{s}$, but vanishes if ${\sigma }_{e^{+}{e}^{-}}$ falls faster.