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

The usual procedure to extract the g(omega rho pi)(eff) effective coupling from experimental data resumes not only the rho meson effect but also all its additional radial excitation modes. In this work, we consider a particular form of the spectrum and relations among the couplings to explicitly add the radial excitations of the rho meson from the omega ->pi(0)gamma and omega -> 3 pi decays. This allows to identify the single g(omega rho pi)= 8.3 +/- 0.8 GeV-1, which is about 40% smaller than the effective g(omega rho pi)(eff). We verify the consistency with the chiral approach in the pi(0) -> gamma gamma and gamma* -> 3 pi processes, exhibiting the role of each contribution. In particular, we show that for the gamma* -> 3 pi decay, the usual relation A(gamma 3 pi)(VMD) = (3/2)A(gamma 3 pi)(WZW), encodes all the vector contributions and not only the rho meson one. In addition, we find that there is a strong (accidental) cancelation between the radial excitations and the contact term contributions.