Production ofJ/ψ+cc¯through two photons ine+e−annihilation

We study the production of $J/\psi +c\overline{c}$ in $e^{+}{e}^{-}$ annihilation through two virtual photons. The cross section is estimated to be 23 fb at $\sqrt{s}=10.6\mathrm{}\mathrm{GeV},$ which is smaller by a factor of 6 than the calculated cross section for the same process but through one virtual photon. As a result, while the annihilation into two photons may be important for certain exclusive production processes, the big difference between the inclusive production cross section $\sigma {(e}^{+}{e}^{-}\to J/\psi +c\overline{c})\simeq 0.9\mathrm{pb}$ observed by Belle and the current nonrelativistic QCD prediction of $\simeq 0.15\mathrm{pb}$ still remains very puzzling. We find, however, that as the center-of-mass energy increases $(\sqrt{s}>20\mathrm{}\mathrm{GeV})$ the production through two virtual photons $e^{+}{e}^{-}\to 2{\gamma }^{*}\to J/\psi +c\overline{c}$ will prevail over that through one virtual photon, because in the former process the photon fragmentation into $J/\psi$ and into the charmed quark pair becomes more important at higher energies.