Fragmentation of charm to charmonium in e ⁺ e ^- and pp collisions

We perform numerical comparison of the fragmentation mechanism of charmonium production (g g → c c¯
followed by c → ψ c) with the full leading order calculation (g g → ψ c c¯ at O(α4
s )). We conclude that the nonfragmentation contributions remain important up to J/ψ
transverse momenta about as large as 40 GeV, thus making
questionable the applicability of the fragmentation approximation at smaller transverse momenta.