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

Motivated by the large cross section of $e^{+}{e}^{-}\to \eta J\mathrm{/}\psi$ process measured by the BESIII and Belle Collaborations recently, we evaluate this process at $\mathcal{O}({\alpha }_s^4)$ accuracy in the framework of nonrelativistic QCD. We find that the cross section at the center-of-mass energy $\sqrt{s}=4.009$ {GeV} is $34.6\mathrm{p}\mathrm{b}$, which is consistent with the BESIII data. The comparison with the Belle data in the region from $4.0
$\mathrm{G}\mathrm{e}\mathrm{V}$$to$5.3\ $\mathrm{G}\mathrm{e}\mathrm{V}$$isalsopresented\mathrm{.}Concerningthe$\eta$and$\eta^\prime$mixingandthepotentialgluoniumcomponentof$\eta^\prime$, we also estimate the rate of $e^{+}{e}^{-}\to {\eta }^{\mathrm{\prime }}J\mathrm{/}\psi$ process, which can be checked within the updated Belle data.