The charmonium production has long been considered as a good process for investigating both perturbative and nonperturbative properties of quantum chromodynamics (QCD), because of the relatively large difference between the scale at which the charm–quark pair is produced at the parton level and the scale at which it evolves into a quarkonium. In particular, comparing to hadron colliders, e+e− colliders, provide a cleaner environment to study the charmonium productions and decays. However, some puzzles arise from the recent measurements on the prompt J/ψ productions at BaBar and Belle [1–3]. For the inclusive J/ψ productions, the cross section is much larger than the predictions of nonrelativistic quantum chromodynamics (NRQCD) [4]; there is also an over-abundance of the four-charm–quark processes including the exclusive J/ψ and charmonium productions; there is no apparent signal in the hard J/ψ spectrum which has been predicted by the J/ψgg production mode as well as the color-octet mechanism in NRQCD. To provide plausible solutions and explanations for these conflicts, theorists have studied the possibilities of the contribution from two-virtual-photon mediate processes [5], large higher-order QCD corrections [6,7], collinear suppression at the end-point region of the J/ψ momentum [7,8], contribution from the J/ψ-glueball associated production [9] and contribution from a very light scalar boson [10].
