Role of meson loops in the f0(1370), f0(1500), and f0(1710) decays into Vγ

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 mesons 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 these observables as a test of the possible glueball nature of this resonance. At the same time we also evaluate the relevance of the same loops in the two lighter scalar mesons, the f(0)(1370) and f(0)(1500), providing information of relevance in the search for the nature of the second nonet of scalar mesons.