Problems of double-charm production in e+e− annihilation at s=10.6 GeV

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 5.5 fb, 6.7 fb, 1.1 fb, and 1.6 fb 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+cc̄ is calculated. In addition, we also evaluate the ratio of exclusive to inclusive production cross sections. The ratio of J/ψηc production to J/ψcc̄ production could be consistent with the experimental data.