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

Abstract

Motivated by the large cross section of $e^{+}{e}^{-}\to \eta J/\psi$ 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 $34.6\mathrm{pb}$, 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 $\eta$ 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 can be checked within the updated Belle data.

Comments: 7 pages, 3 figures, and 1 table; to appear in PRD