Transverse momentum dependent shape function for $J/ψ$ production in SIDIS

Kavli Affiliate: Feng Yuan

| First 5 Authors: Daniël Boer, Jelle Bor, Luca Maxia, Cristian Pisano, Feng Yuan

| Summary:

It has been shown previously that the transverse momentum dependent (TMD)
factorization of heavy quarkonium production requires a TMD shape function. Its
perturbative tail can be extracted by matching the cross sections valid at low
and high transverse momenta. In this article we compare the order-$alpha_s$
TMD expressions with the order-$alpha_s^2$ collinear ones for $J/psi$
production in semi-inclusive deep inelastic scattering (SIDIS), employing
nonrelativistic QCD in both cases. In contrast to previous studies, we find
that the small transverse momentum limit of the collinear expressions contain
discontinuities. We demonstrate how to properly deal with them and include
their finite contributions to the TMD shape functions. Moreover, we show that
soft gluon emission from the low transverse momentum Born diagrams provide the
same leading order TMD shape functions as required for the matching. Their
revised perturbative tails have a less divergent behaviour as compared to the
TMD fragmentation functions of light hadrons. Finally, we investigate the
universality of TMD shape functions in heavy quarkonium production, identify
the need for process dependent factorization and discuss the phenomenological

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