Quarkonium TMD fragmentation functions in NRQCD

Abstract

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, $$ \mathcal{O}\left({\alpha}_s^2\right) $$ O α 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.