Chiral perturbation theory vs. vector meson dominance in the decays $\phi \to \rho \gamma \gamma$ and $\phi \to \omega \gamma \gamma$

It is pointed out that the radiative decays of a $\phi$ meson, $\phirho$ and $\phiom$, receive dominant contributions from the pseudoscalar ($P = \eta, \eta^{'}$) exchanges. Using the vector meson dominance model, we find that $B (\phirho) \approx 1.3 \times 10^{-4}$ and $B (\phiom) \approx 1.5 \times 10^{-5}$, which are mainly from the $\eta^{'}$ pole. Thus, these decays are well within the reach of the $\phi$ factory. Our estimates are a few orders of magnitude larger than the chiral loop contributions in the heavy vector meson chiral lagrangian, which is about ( a few ) $\times 10^{-9}$.