We calculate the next-to-leading-order (NLO) QCD correction to $e^{+}{e}^{-}\to J/\psi c\overline{c}$ at the $B$ factories, and present theoretical predictions on the momentum and production angular distribution for $J/\psi$ production, and momentum distribution for $J/\psi$ polarization at NLO for the first time. By applying Brodsky, Lepage, and Mackenzie scale setting for the renormalization scale, it is found that the QCD perturbative expansion is significantly improved with the unique scale choice ${\mu }^{*}=1.65\mathrm{GeV}$. Together with the ${\psi }^{\prime }$ feed-down contribution, the total cross section and momentum distribution can account for the recent experimental measurement by the Belle collaboration. The total cross section and momentum distribution are also found to be consistent with the experimental measurement in the previous study on $e^{+}{e}^{-}\to J/\psi gg$. However, the production angular distribution of $J/\psi$ production for either the $J/\psi c\overline{c}$ or the $J/\psi gg$ channel has a quite different shape in contrast with the new experimental data, although it fits with the experimental data when the two channels are added together. This situation is difficult to explain. To clarify the puzzle of $J/\psi$ polarization, further experimental measurements are strongly expected to testify our predictions on the momentum distribution for $J/\psi$ polarization. Our total cross section agrees with that given in the previous study of Zhang and Chao by using their renormalization scheme and input parameters.

• Received 7 April 2009

DOI:https://doi.org/10.1103/PhysRevD.80.054015