Search for the scalar $a_0$ and $f_0$ mesons in the reactions $e^{+}{e}^{-}\to \gamma {\pi }^0{\pi }^0\left(\eta \right)$

It is shown that the reactions $e^{+}{e}^{-}\to \gamma {\pi }^0{\pi }^0\left(\eta \right)$ give a good chance for observing the scalar $a_0$ and $f_0$ mesons. In the photon energy region less than 100 MeV the vector meson contributions $e^{+}{e}^{-}\to V^0\to {\pi }^0{V}^{\prime 0}\to \gamma {\pi }^0{\pi }^0\left(\eta \right)$ are negligible in comparison with the scalar meson $e^{+}{e}^{-}\to \phi$ $\to \gamma f_0{(a}_0)\to \gamma {\pi }^0{\pi }^0(\eta )$ for $B(\phi \to \gamma f_0{(a}_0)\to \gamma {\pi }^0{\pi }^0\left(\eta \right))$ greater than $5\times {10}^{-6}$ ${(10\mathrm{}}^{-5}).\mathrm{}$ Using the two-channel treatment of the ππ scattering the predictions for $B(\phi \to \gamma {(f}_0+\sigma )\to \gamma \pi \pi )$ are derived. The four-quark model, the model of the $K\overline{K}$ molecule, and the $s\overline{s}$ model of scalar $f_0$ and $a_0$ mesons are discussed.