Scalar f0(980) and sigma(500) meson exchange in phi decays into pi0pi0gamma

The complementarity between Chiral Perturbation Theory and the Linear Sigma Model is exploited to study $\pi^0\pi^0$ production in $\phi$ radiative decays, where the effects of the $f_0(980)$ scalar resonance, and those of its more controversial $\sigma(500)$ partner, should become manifest via the $\phi\to K^+ K^- (\gamma)\to\pi^0\pi^0\gamma $ decay chain. The recently reported data on $\phi\to\pi^0\pi^0\gamma$ coming from the VEPP-2M $e^+ e^-$ collider in Novosibirsk and the DA$\Phi$NE $\phi$-factory in Frascati can be reasonably described in our approach, which we propose as a promising first step towards more detailed analyses. The $f_0(980)$ contribution, which appears as a moderately narrow peak at the high part of the dipion mass spectrum, can be interpreted as the isoscalar member of the scalar nonet with a large $f_0 K\bar{K}$ coupling and an $f_0\pi\pi$ coupling suppressed by almost ideal $\sigma$-$f_0$ mixing. Indeed, the mixing angle in the flavour basis is found to be $\phi_{S}\approx -6^\circ$, if the $f_0$-propagator is approximated by a simple Breit-Wigner, or $\phi_{S}\approx -9^\circ$, if an improved two-channel analysis is performed. The $\sigma(500)$ resonance, which is then strongly coupled to pion pairs, yields a tiny contribution because, in our approach, its coupling to kaon pairs is proportional to $m^2_\sigma-m^2_K$ and thus quite small.