Lightest scalar resonances and the dynamics of the $\gamma\gamma\to\pi\pi$ reactions

The high-statistics Belle data on the $\gamma\gamma\to\pi^+\pi^-$ and $\gamma\gamma\to\pi^0\pi^0$ reactions have been jointly analyzed. The main dynamical mechanisms of these reactions for energies below $1.5$ GeV have been revealed. It has been shown that the direct coupling constants of the $\sigma(600)$ and $f_0(980)$ resonances with a $\gamma\gamma$ pair are small and that the $\sigma(600)\to\gamma\gamma$ and $f_0(980)\to\gamma\gamma$ decays are four-quark transitions due primarily to $\pi^+\pi^-$- and $K^+K^-$-loop mechanisms, respectively. The role of the chiral shielding of the $\sigma(600)$ resonance is emphasized. The widths of the $f_0(980)\to\gamma\gamma$ and $\sigma(600)\to\gamma\gamma$ decays averaged over the resonance mass distributions, as well as the width of the $f_2(1270)\to\gamma\gamma$ decay, are estimated as $\langle\Gamma_{f_0\to\gamma \gamma}\rangle_{\pi\pi}\approx 0.19$ keV, and $\langle\Gamma_{\sigma \to\gamma\gamma}\rangle_{\pi\pi}\approx 0.45$ keV, $\Gamma_{f_2\to\gamma\gamma}(m^2_{f_2})\approx 3.8$ keV.