Gluon TMD fragmentation function into quarkonium

TL;DR

This paper calculates the gluon TMD fragmentation function into heavy quarkonium at NLO, clarifying divergence cancellations and matching to integrated FF, aiding precise quarkonium production studies.

Contribution

It provides the first NLO computation of gluon TMDFF into quarkonium in the color-octet channel, including divergence cancellation and matching to integrated FF.

Findings

Explicit cancellation of rapidity divergences in TMDFF.

Matching coefficient aligns with theoretical expectations.

Results facilitate accurate quarkonium transverse-momentum phenomenology.

Abstract

We compute the gluon transverse-momentum-dependent fragmentation function (TMDFF) at next-to-leading order (NLO) into heavy quarkonium in the color-octet $^3S_1^{[8]}$ channel, based on the NRQCD factorization approach. The spurious rapidity divergences are explicitly shown to cancel in a well-defined TMDFF, which incorporates the needed soft factor. We also compute the integrated gluon FF at NLO in the same $^3S_1^{[8]}$ channel, and show that the matching coefficient of the TMDFF onto the FF at large transverse momentum is the expected one. These results are relevant to perform precise and sensible phenomenological studies of transverse-momentum spectra of quarkonium production, for which the production mechanism through fragmentation plays a relevant role, like in the future Electron-Ion Collider.