D. Garcia Gudino, G. Toledo Sanchez
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.
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http://arxiv.org/abs/1209.6565
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