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

TL;DR

This paper investigates the impact of including an infinite spectrum of rho meson excitations on anomalous decay processes, revealing how these excitations influence effective couplings and decay amplitudes.

Contribution

It explicitly incorporates rho meson radial excitations into decay models, clarifying their effects on effective couplings and decay relations, and demonstrating cancellations with contact terms.

Findings

Effective coupling g_{ωρπ} is 40% smaller than the effective value.

Radial excitations and contact terms nearly cancel each other.

The usual VMD relation encodes all vector contributions, not just rho meson.

Abstract

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.