Search for $a_0(980)$ and $f_0(980)$ mesons in $\varphi \to \gamma K\bar{K}$

We study the decay $\varphi \to \gamma K^{+}{K}^{-}$ taking into account the scalar mesons production $\varphi \to \gamma (f_0+a_0)\to \gamma K^{+}{K}^{-}$ and the final state radiation. We note that the relative sign between the final state radiation amplitude and the scalar meson production amplitude is fixed in the $K^{+}{K}^{-}$ loop model which describes data on the $\varphi \to \gamma f_0\to \gamma \pi \pi$ and $\varphi \to \gamma a_0\to \gamma \pi \eta$ decays. As consequence this model predicts the definite interference between the final state radiation and the scalar resonance production amplitudes. We calculate the mass spectra of the $\varphi \to \gamma K^{+}{K}^{-}$ decay and the differential cross-sections for $e^{+}{e}^{-}\to \varphi \to \gamma K^{+}{K}^{-}$ and for $e^{+}{e}^{-}\to \varphi \to \gamma K^0{\bar{K}}^0$ reactions.