We make a detailed study on the typical production channel of double charmoniums, $e^+e^-\to J/\psi+\eta_c$, at the center-of-mass collision energy $\sqrt{ s}=10.58$ GeV. The key component of the process is the form factor $F_{ \rm VP}(q^2)$, which has been calculated within the QCD light-cone sum rules (LCSR). To improve the accuracy of the derived LCSR, we keep the $J/\psi$ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for $e^+e^-\to J/\psi+\eta_c$ at three typical factorization scales are $\sigma|_{ \mu_s} = 22.53^{ +3.46}_{ -3.49}~{ \rm fb}$, $\sigma|_{ \mu_k} = 21.98^{ +3.35}_{ -3.38}~{ \rm fb}$ and $\sigma|_{ \mu_0} = 21.74^{ +3.29}_{ -3.33}~{ \rm fb}$, respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors.
Categories: hep-ph