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

TL;DR

This paper compares the fragmentation mechanism of charmonium production with full leading order calculations in high-energy collisions, finding non-fragmentation effects remain significant up to high transverse momenta, questioning the fragmentation approximation's validity.

Contribution

It provides a numerical comparison between fragmentation and full leading order calculations for charmonium production, highlighting the importance of non-fragmentation contributions.

Findings

Non-fragmentation contributions are significant up to 50 GeV transverse momentum.

Fragmentation approximation may not be valid at lower transverse momenta.

Full leading order calculations are necessary for accurate predictions.

Abstract

We perform numerical comparison of the fragmentation mechanism of charmonium production ($g\,g\to c\,\bar{c}$ followed by $c\to\psi\,c$) with the full leading order calculation ($g\,g\to\psi\,c\,\bar{c}$ at ${\O} (\alpha_s^4)$). We conclude that the non-fragmentation contributions remain important up to $J/\psi$ transverse momenta about as large as 50 GeV, thus making questionable the applicability of the fragmentation approximation at smaller transverse momenta.