On the role of meson loops in the $f_0(1710)$ decay into $V\gamma$

Abstract

We investigate the relevance of the meson loops in the $f_0(1710)$ scalar meson decay into one photon and one vector meson, ($\rho$, $\omega$ and $\phi$). In particular we estimate the size of the loops coming from the decay of the $f_0(1710)$ into two pseudoscalar mesons, containing three pseudoscalar mesons in the loop or two pseudoscalar and one vector meson. The results, despite having large uncertainties, manifest that the contribution of the meson loops to these radiative decays is quite relevant and should be taken into account by the theoretical calculations which use this observables as a test of the possible glueball nature of this resonance.