Revisiting the production of $J/\ddot{I}ˆ+\hat{I}{\cdot }_c$ via the $e^{+}{e}^{-}$ annihilation within the QCD light-cone sum rules

Abstract

We make a detailed study on the typical production channel of double charmoniums, $e^{+}{e}^{-}\to J/\ddot{I}ˆ+\hat{I}{\cdot }_c$, at the center-of-mass collision energy $\sqrt{s}=10.58$ GeV. The key component of the process is the form factor $F_{\mathrm{VP}}(q^2)$, which has been calculated within the QCD light-cone sum rules (LCSR). To improve the accuracy of the derived LCSR, we keep the $J/\ddot{I}ˆ$ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for $e^{+}{e}^{-}\to J/\ddot{I}ˆ+\hat{I}{\cdot }_c$ at three typical factorization scales are $\ddot{I}ƒ{|}_{\hat{I}{¼}_s}=22.53_{-3.49}^{+3.46}\mathrm{fb}$, $\ddot{I}ƒ{|}_{\hat{I}{¼}_k}=21.98_{-3.38}^{+3.35}\mathrm{fb}$ and $\ddot{I}ƒ{|}_{\hat{I}{¼}_0}=21.74_{-3.33}^{+3.29}\mathrm{fb}$, respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors.

8 pages, 3 figures, version to be published in Physical Review D