Problems of Double Charm Production in e+e- Annihilation at √s=10.6 GeV

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Using the nonrelativistic QCD(NRQCD) factorization formalism, we calculate the color-singlet cross sections for exclusive production processes e++e-→ J/ψ+ηc and e++e-→ J/ψ+ χcJ (J=0,1,2) at the center-of-mass energy √s=10.6 GeV. The cross sections are estimated to be 5.5fb, 6.7fb, 1.1fb, and 1.6fb for ηc, χc₀, χc₁ and χc₂, respectively. The calculated J/ψ+ηc 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 O(α²ₛ) color-singlet cross section for e++e-→ χc₀+ c c is calculated. In addition, we also evaluate the ratio of exclusive to inclusive production cross sections. The ratio of J/ψηc production to J/ψcc production could be consistent with the experimental data.