To What Extent Should We Resort to the Color-Octet Mechanism in Explaining the Tevatron Large-p_T Data?

We revisit the direct production of $J/\psi(\psi')$ at large transverse momentum, $p_T \gg M_{J/\psi}$, at the Fermilab Tevatron. It is found that the sea quark participated processes, together with the fragmentation mechanism, dominate the charmonium production within the framework of color-singlet model, which were overlooked in previous investigations. The new result may help to explain the large-$p_T$ $J/\psi(\psi')$ data observed by the CDF experiment group in conventional quarkonium production scheme, the color-singlet model; or at least reduce the contribution from color-octet mechanism. In that sense, the difficulty which color-octet mechanism meets in explaining the large-$p_T$ $J/\psi(\psi')$ polarization events is alleviated, or even disappeared