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.
Highlights
Double charmonium production at the B-factories has attracted large attention of experimentalists and theorists for a long time
The key component of the process is the form factor FVPðq2Þ, which has been calculated within the QCD light-cone sum rules (LCSR)
Those measurements have severe discrepancy with the leading-order predictions based on the nonrelativistic QCD (NRQCD) factorization theory, which are within the range of 2.3–5.5 fb [4,5,6]
Summary
Double charmonium production at the B-factories has attracted large attention of experimentalists and theorists for a long time. The BABAR Collaboration issued their measured value σðeþe− → J=ψ þ ηcÞ × B≥2 1⁄4 17.6 Æ 2.8þ−21..15 fb [3] Those measurements have severe discrepancy with the leading-order predictions based on the nonrelativistic QCD (NRQCD) factorization theory, which are within the range of 2.3–5.5 fb [4,5,6]. The electromagnetic form factor FVPðq2Þ dominates the lightcone formalism, which can be calculated by using the QCD light-cone sum rules (LCSRs). [19], after applying the operator production expansion (OPE) near the light cone and taking the ηc leading-twist LCDA into account, the authors obtained a large factorization scale–. A physical observable should be independent to the choice of factorization scale, and in the present paper, we shall adopt the LCSR approach to reanalyze the process and its factorization scale dependence.
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