New extraction of color-octet NRQCD matrix elements from charmonium hadroproduction

We re-analyze Tavatron data on charmonium hadroproduction in the framework of the color-octet model implemented in the event generator PYTHIA taking into account initial-state radiation of gluons and Altarelli-Parisi evolution of final-state gluons fragmenting into $c\bar{c}$ pairs. We obtain new values for the color-octet matrix elements relevant to this production process. We discuss the sensitivity of our results to the transverse momentum lower cut-off employed in the generation to avoid the problematic $p_t{\to}0$ region, arguing about the reliability of our previous extraction of the NRQCD matrix elements for the $^3S_1^{(8)}$ and $^1S_0^{(8)}+^3P_J^{(8)}$ contributions. Finally we extrapolate to LHC energies to get predictions on the $J/\psi$ direct production rate.