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

Abstract

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

Comments: 31 pages, 10 ps files of figures, minor numerical changes, Appendix corrected, to be published in Phys.Rev.D