# Scalar *f*_{ 0 }(980) and \(\sigma (500)\) meson exchange in \(\phi\) decays into \(\pi^0\pi^0\gamma\)

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## Abstract.

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 \(\phi\rightarrow K^+ K^- (\gamma)\rightarrow\pi^0\pi^0\gamma \) decay chain. The recently reported data on \(\phi\rightarrow\pi^0\pi^0\gamma\) 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 flavor basis is found to be \(\phi_{S}\approx - 6^\circ\), if the f_{0} propagator is approximated by a simple Breit-Wigner expression, 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.

## Keywords

Sigma Model Narrow Peak Radiative Decay Decay Chain Chiral Perturbation Theory## Preview

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