Color-singlet direct J/\psi and \psi' production at Tevatron in the k_t factorization approach

Direct $J/\psi$ and $\psi'$ production rates at Tevatron are calculated in the $k_t$-factorization approach within the color-singlet model. In this approach, the production rates are enhanced by a factor of 20 compared to the naive collinear parton model. However, the theoretical predictions are still below the experimental data by at least one order of magnitude. This means that to explain charmonium productions at Tevatron, we still need to call for the contributions from color-octet channels or other production mechanisms.