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 c̅ followed by c→ψ c ) with the full leading order calculation ( g g→ψ c c̅ at 𝒪(α _s^4) ). We conclude that the non-fragmentation 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.