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Cross section for double charmonium production in electron-positron annihilation at energy $\sqrt{s}$= 10.6 GeV

In this work we study the process $e^{+}+e^{-}\longrightarrow J/Ψ+η_{c} $ at energy $\sqrt{s}= 10.6 GeV$ observed recently at B-factories whose measurements were made by Babar and Belle groups. We calculate the cross section for this process in the Bethe-salpeter formalism under Covariant Instantaneous Anstaz (CIA). To simplify our calculation, the heavy quark approximation $(q<<M, P M)$ is employed in the quark and gluon propagators. In the exclusive process of $e^{+}e^{-}$ annihilation into two heavy quarkonia, the cross section calculated in this scenario is compatible with the experimental data of Babar and Belle.