We study the J/ψ pair production issue at the Fermilab Tevatron Run II with a center-of-mass energy of s^（1/2）=1.96TeV. Both the color-singlet and color-octet production mechanisms are considered. Our results show that the transverse momentum （pT） scaling behaviors of the double J/ψ differential cross-sections in the color-singlets and color-octets deviate distinctively from each other while pT is larger than 8GeV, and with a luminosity of 5fb^-1 , the J/ψ pair events from the color-singlet scheme are substantially measurable in the Tevatron experiments, even with a certain lower transverse momentum cut. Hence the Tevatron is still a possible platform to check the heavy quarkonium production mechanism.
We calculate the next-to-leading order （NLO） quantum chromodynamics （QCD） corrections to double charmonium production processes e^＋e^- → γ＊ →ηc＋hc（1P）/ψ1,2（1D） within the non-relativistic QCD （NRQCD） factorization framework. We find that the corrections to ηc＋hc（1P） production are positive, while those to ηc＋ψ1/2（1D） are negative. Unlike the J/ψ＋ηc case, all the corrections here are not large. Uncertainties in the renormalization scale, quark mass and running energy of center-of-mass are discussed, and the scale dependence of these processes is found to be greatly reduced with the NLO QCD corrections.
