Using the nonrelativistic QCD(NRQCD) factorization formalism, we calculate the color-singlet cross sections for exclusive production processes ${ e^++e^-\to J/\psi+\eta_c}$~ and ~$e^++e^-\to J/\psi + \chi_{ cJ}$~$(J=0,1,2)$ 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 $\eta_c, \chi_{ c0}, \chi_{ c1}$ and $\chi_{ c2}$, respectively. The calculated $J/\psi+\eta_c$ 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}$$(\alpha^2_{ s})$ color-singlet cross section for ${ e^++e^-\to \chi_{ c0}+ c\bar { c}}$ is calculated. In addition, we also evaluate the ratio of exclusive to inclusive production cross sections. The ratio of $J/\psi\eta_c$ production to $J/\psi c\bar{ c}$ production could be consistent with the experimental data.
Categories: hep-ph