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Motivated by the large cross section of $e^+e^-\to \eta J/\psi$ processmeasured by the BESIII and Belle Collaborations recently, we evaluate thisprocess at $\mathcal{O}(\alpha_s^4)$ accuracy in the framework ofnonrelativistic QCD. We find that the cross section at the center-of-massenergy $\sqrt{s}=4.009$ {GeV} is $34.6\mathrm{pb}$, which is consistent withthe BESIII data. The comparison with the Belle data in the region from $4.0\\mathrm{GeV}$ to $5.3\ \mathrm{GeV}$ is also presented. Concerning the $\eta$and $\eta^\prime$ mixing and the potential gluonium component of $\eta^\prime$,we also estimate the rate of $e^+e^-\to \eta^\prime J/\psi$ process, which canbe checked within the updated Belle data.

Understanding the cross section of $e^+e^-\to \eta J/\psi$ process via nonrelativistic QCD