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Both hard and soft QCD dynamics are important in charmonium production, aspresented here through a next-to-leading order QCD matrix element calculationcombined with the colour evaporation model. Observed $x_F$ and $p_\perp$distributions of $J/\psi$ in hadroproduction at fixed target and $p\bar{p}$collider energies are reproduced. Quite similar results can also be obtained ina more phenomenologically useful Monte Carlo event generator where theperturbative production of \ccbar pairs is instead obtained through leadingorder matrix elements and the parton shower approximation of the higher orderprocesses. The soft dynamics may alternatively be described by the soft colourinteraction model, originally introduced in connection with rapidity gaps. Wealso discuss the relative rates of different charmonium states and introduce animproved model for mapping the continuous \ccbar mass spectrum on the physicalcharmonium resonances.Comment: 21 pages, 13 eps figure

Soft and hard QCD dynamics in hadroproduction of charmonium