We make a detailed study on the typical production channel of double charmoniums, e + e ? → J / ψ + η c , at the center-of-mass collision energy s = 10.58 ? ? GeV . The key component of the process is the form factor F 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 / ψ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for e + e ? → J / ψ + η c at three typical factorization scales are σ | μ s = 22.5 3 ? 3.49 + 3.46 ? ? fb , σ | μ k = 21.9 8 ? 3.38 + 3.35 ? ? fb , and σ | μ 0 = 21.7 4 ? 3.33 + 3.29 ? ? fb , respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors.
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