About the inclusion of an infinite number of resonances in anomalous   decays
  The extracted value for the $g^{eff}_{\omega \rho\pi}$ effective coupling from experimental data, considering only the $\rho$ meson, resumes not only the $\rho$ meson effect but also all its additional radial excitation modes. By explicitly adding the radial excitations of the $\rho$ meson, considering a particular form of the spectrum and relations among the couplings, we identify the single $g_{\omega \rho \pi}$ and the $\rho$ radial excitations effect in the $\omega \rightarrow \pi^0 \gamma$ decay. We obtain that the individual coupling is in the range $g_{\omega\rho\pi}= 8.2 - 8.6 {\text GeV}^{-1}$, which is about 40% smaller than the effective $g^{eff}_{\omega\rho\pi}$. We verify the consistency with the chiral approach in the $\pi^0 \rightarrow \gamma\gamma$ and $\gamma^* \rightarrow 3\pi$ processes. Besides the model dependence, our description succeeds in exhibiting how each contribution came into the game. In particular, we show that for the $\gamma^* \rightarrow 3 \pi$ decay, the usual relation $\mathcal{A}^{VMD}_{\gamma3\pi}=(3/2)\mathcal{A}^{WZW}_{\gamma3\pi}$, encodes all the vector contributions and not only the $\rho$ meson one. In addition, we find that there is an almost exact (accidental) cancelation between the radial excitations and the contact term contributions. 
D. Garcia Gudino and G. Toledo Sanchez
nucl-th hep-ph