Comment on vector-meson dominance and theγ→3πvertex in the low-energy limit

It is found that a simple derivation of a relation between the $\gamma \to 3\pi$ and ${\pi }^{\circ }\to 2\gamma$ vertices, previously obtained from current algebra and the partial-conservation-of-axial-vector-current anomaly, can be given on the basis of a pole model together with vector-meson dominance if we require consistency between a $\rho$-pole description of $\pi \pi$ scattering in the framework of a Yang-Mills theory and a theorem of Weinberg for the same process in the two-soft-pion limit.