ar X iv : h ep - p h / 03 05 08 4 v 1 8 M ay 2 00 3 Production of J / ψ + cc̄ through two photons in e + e − annihilation

We study the production of J/ψ + cc̄ in ee annihilation through two virtual photons. The cross section is estimated to be 23 fb at √ s = 10.6 GeV, which is smaller by a factor of six 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 gap between the inclusive production cross section σ(ee → J/ψ+cc̄) ≃ 0.9pb observed by Belle and the current nonrelativistic QCD prediction of ≃0.15pb still remains very puzzling. We find, however, as the center-of-mass energy increases ( √ s > 20 GeV) the production through two virtual photons ee → 2γ∗ → J/ψ + cc̄ will prevail over that through one virtual photon, because in the former process the photon fragmentation into J/ψ and into the charmed quark pair becomes more important at higher energies. PACS number(s): 12.40.Nn, 13.85.Ni, 14.40.Gx Charmonium production is one of the important processes to test quantum chromodynamics (QCD) both perturbatively and non-perturbatively. Because of the simpler parton structure involved, which will reduce the theoretical uncertainty, charmonium production in ee annihilation is expected to be more decisive in clarifying the production mechanisms of heavy quarkonia. The two B factories with BaBar and Belle are collecting huge data samples of continuum ee annihilation events, which will allow us to have a fine data analysis for charmonium production. Recently, Charmonium production in ee annihilation has become more interesting and puzzling, because of the large gap between the Belle measurements[1, 2] and the theoretical calculations for both inclusice[3, 4, 5, 6] and exclusive [7, 8] charmonium production via double cc̄ pairs based on nonrelativistic QCD (NRQCD). For the inclusive processes, Belle has reported a measurement on the J/ψ production in ee annihilation at √ s = 10.6 GeV[1, 2], and found that a very large fraction of the produced J/ψ is due to the double cc̄ production in ee annihilation[1] σ(ee → J/ψcc̄)/σ(ee → J/ψX) = 0.59 −0.13 ± 0.12, (1)