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 $\varphi$ 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 $\varphi \to {\pi }^0{\pi }^0\gamma$ coming from the VEPP-2M $e^{+}{e}^{-}$ collider in Novosibirsk and the DA$\mathrm{\Phi }$NE $\varphi$-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 $f_0 K\bar{K}$couplingandan$f_0\pi\pi$couplingsuppressedbyalmostideal$\sigma$-$f_0$ mixing. Indeed, the mixing angle in the flavour basis is found to be ${\varphi }_S\approx -6^{\circ }$, if the $f_0$-propagator is approximated by a simple Breit-Wigner, or ${\varphi }_S\approx -9^{\circ }$, 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 $m_{\sigma }^2-m_K^2$ and thus quite small.