Understanding the cross section of $e^+e^-\to ηJ/ψ$ process via nonrelativistic QCD

Motivated by the large cross section of $e^+e^-\to ηJ/ψ$ process measured by the BESIII and Belle Collaborations recently, we evaluate this process at $\mathcal{O}(α_s^4)$ 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 $34.6\mathrm{pb}$, which is consistent with the 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 $η$ and $η^\prime$ mixing and the potential gluonium component of $η^\prime$, we also estimate the rate of $e^+e^-\to η^\prime J/ψ$ process, which can be checked within the updated Belle data.

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