Revisiting the production of $J/\psi+\eta_c$ via the $e^+e^-$ annihilation within the QCD light-cone sum rules

TL;DR

This paper calculates the $J/ar{J}$ production cross section in $e^+e^-$ collisions at 10.58 GeV using QCD light-cone sum rules, incorporating twist-4 distribution amplitudes, and finds results consistent with experimental data.

Contribution

It provides a refined calculation of the $J/ar{J}$ production form factor using twist-4 accuracy in light-cone sum rules, improving theoretical predictions.

Findings

Cross sections around 22 fb at different scales

Small dependence on factorization scale

Results agree with BABAR and Belle measurements

Abstract

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.