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The extracted value for the $g^{eff}_{\omega \rho\pi}$ effective couplingfrom experimental data, considering only the $\rho$ meson, resumes not only the$\rho$ meson effect but also all its additional radial excitation modes. Byexplicitly adding the radial excitations of the $\rho$ meson, considering aparticular form of the spectrum and relations among the couplings, we identifythe single $g_{\omega \rho \pi}$ and the $\rho$ radial excitations effect inthe $\omega \rightarrow \pi^0 \gamma$ decay. We obtain that the individualcoupling is in the range $g_{\omega\rho\pi}= 8.2 - 8.6 {\text GeV}^{-1}$, whichis about 40% smaller than the effective $g^{eff}_{\omega\rho\pi}$. We verifythe consistency with the chiral approach in the $\pi^0 \rightarrow\gamma\gamma$ and $\gamma^* \rightarrow 3\pi$ processes. Besides the modeldependence, our description succeeds in exhibiting how each contribution cameinto the game. In particular, we show that for the $\gamma^* \rightarrow 3 \pi$decay, the usual relation$\mathcal{A}^{VMD}_{\gamma3\pi}=(3/2)\mathcal{A}^{WZW}_{\gamma3\pi}$, encodesall the vector contributions and not only the $\rho$ meson one. In addition, wefind that there is an almost exact (accidental) cancelation between the radialexcitations and the contact term contributions.

About the inclusion of an infinite number of resonances in anomalous decays