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We calculate the cross section of the exclusive process $e^{+} +e^{-}\toJ/\psi+\eta_c$ at the leading order approximation within the QCD light-cone sumrules (LCSR) approach. It is found that the form factor$F_{VP}(V=J/\psi,P=\eta_c)$ depends mainly on the behavior of the twist-2distribution amplitude of the $\eta_c$-meson at the scale of this process. Thusin order to obtain a reliable estimation of the cross section, it is importantto have a realistic distribution amplitude of the $\eta_c$ meson, and to dealwith the evolution of the distribution amplitude to the effective energy scaleof the process. Our results show that one can obtain a compatible predictionwith the Belle and BarBar experimental data.

The cross section of the process $e^{+}+e^{-}\to J/\psi+\eta_c$ within the QCD light-cone sum rules