Quarkonium TMD fragmentation functions in NRQCD

TL;DR

This paper investigates the transverse-momentum-dependent fragmentation functions of quarkonium in NRQCD, deriving a new factorization theorem and comparing production mechanisms relevant for electron-ion collider experiments.

Contribution

It introduces a new factorization theorem involving quarkonium TMD fragmentation functions in NRQCD and calculates their matching to non-perturbative matrix elements at lowest order.

Findings

Identifies phase space regions where photon-gluon fusion or light-quark fragmentation dominate.

Derives the factorization theorem for light-quark initiated quarkonium production.

Provides a phenomenological comparison relevant for electron-ion collider studies.

Abstract

We study the transverse-momentum spectrum of quarkonium production from single light-parton fragmentation mechanism. In the case of semi-inclusive deep inelastic scattering, we observe that there are two possible initiating processes, namely photon-gluon fusion and light-quark fragmentation. For the second case we derive the factorization theorem, which involves a new hadronic quantity: the quarkonium transverse-momentum-dependent fragmentation functions in NRQCD. We calculate their matching onto the non-perturbative long distance matrix elements at the lowest order in the strong-coupling constant (${\mathcal O}(\alpha_s^2)$). Focusing on the case of the electron-ion collider, we make a comparative phenomenological study of the two production mechanisms and find the regions of the phase space where one is dominant over the other.