s=1.96 TeV. Both the color-singlet and color-octet production mechanisms are considered. Our results show that the transverse momentum (pT) scaling behaviors of the double m J/ψ differential cross-sections in the color-singlets and color-octets deviate distinctively from each other while pT is larger than 8 GeV, and with a luminosity of 5 fb-1, the m 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."> J/ψ pair production at the Tevatron with <I>s</I>=1.96 TeV -
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