About the inclusion of an infinite number of resonances in anomalous decays
Abstract
The extracted value for the
g
eff
ωρπ
effective coupling from experimental data, considering only the
ρ
meson, resumes not only the
ρ
meson effect but also all its additional radial excitation modes. By explicitly adding the radial excitations of the
ρ
meson, considering a particular form of the spectrum and relations among the couplings, we identify the single
g
ωρπ
and the
ρ
radial excitations effect in the
ω→
π
0
γ
decay. We obtain that the individual coupling is in the range
g
ωρπ
=8.2−8.6
GeV
−1
, which is about 40% smaller than the effective
g
eff
ωρπ
. We verify the consistency with the chiral approach in the
π
0
→γγ
and
γ
∗
→3π
processes. Besides the model dependence, our description succeeds in exhibiting how each contribution came into the game. In particular, we show that for the
γ
∗
→3π
decay, the usual relation
A
VMD
γ3π
=(3/2)
A
WZW
γ3π
, encodes all the vector contributions and not only the
ρ
meson one. In addition, we find that there is an almost exact (accidental) cancelation between the radial excitations and the contact term contributions.