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

In this work we study the process $e^{+}+e^{-}⟶J\mathrm{/}\mathrm{\Psi }+{\eta }_c$ at energy $\sqrt{s}=10.6GeV$ 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 $(q<<M,PM)$ 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.