Abstract
Predictions for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD (NRQCD) approach. The predicted cross section is smaller by an order of magnitude than the experimentally observed cross section. We study the process by taking charm quark as a light quark and use light-cone wave functions to parameterize nonperturbative effects related to charmonia. The total cross section of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ can be predicted, if these wave functions are known. Motivated by studies of light-cone wave functions of light hadrons, we make a reasonable assumption of the forms of light-cone wave functions. With these light-cone wave functions we can obtain the cross section which is closer to the experimentally observed than that from the NRQCD approach. We also discuss in detail the difference between two approaches.
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