Problems of Double Charm Production in $e^+e^-$ Annihilation at $\sqrt{s}=10.6$ GeV

Using the nonrelativistic QCD(NRQCD) factorization formalism, we calculate the color-singlet cross sections for exclusive production processes ${e^++e^-\to J/ψ+η_c}$~ and ~$e^++e^-\to J/ψ+ χ_{cJ}$~$(J=0,1,2)$ at the center-of-mass energy $\sqrt{s}$=10.6 GeV. The cross sections are estimated to be 5.5fb, 6.7fb, 1.1fb, and 1.6fb for $η_c, χ_{c0}, χ_{c1}$ and $χ_{c2}$, respectively. The calculated $J/ψ+η_c$ production rate is smaller than the recent Belle data by about an order of magnitude, which might indicate the failure of perturbative QCD calculation to explain the double-charmonium production data. The complete $\cal{O}$$(α^2_{s})$ color-singlet cross section for ${e^++e^-\to χ_{c0}+ c\bar {c}}$ is calculated. In addition, we also evaluate the ratio of exclusive to inclusive production cross sections. The ratio of $J/ψη_c$ production to $J/ψc\bar{c}$ production could be consistent with the experimental data.

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