  We firstly examine hadroproduction of prompt J/psi's at the Fermilab Tevatron
in a Monte Carlo Framework by means of the event generator PYTHIA 5.7 in which
those colour-octet matrix elements processes relevant for charmonium production
have been implemented accordingly. We find that colour-octet matrix elements
presented in literature from p-pbar collider data are systematically
overestimated due to overlooking of the effective primordial transverse
momentum of partons (i.e. including higher-order QCD effects). We estimate the
size of these effects using different parton distribution functions. Finally,
after normalization to Tevatron data, we extrapolate up to LHC energies making
a prediction on the expected pt differential cross-section for charmonium.
