We investigate the feasibility of exploring the gluon transverse-momentum-dependent distribution functions (TMDs) inside a longitudinally polarized nucleon. We utilize quarkonium production via the color-octet mechanism combined with TMD formalism in semi-inclusive deeply inelastic scattering (SIDIS) at low transverse momentum as a tool to access polarized gluon TMDs. The corresponding cross-section of the process is expressed in terms of gluon TMDs and non-relativistic QCD matrix elements. We provide the expressions for the sin2ϕ azimuthal asymmetries of J/ψ production in SIDIS with a unpolarized beam colliding on longitudinally polarized nucleon. The asymmetry is contributed by the time-reversal-odd gluon TMD h1L⊥g(x,pT2). The maximum possible asymmetry deduced from the positivity bound is sizable and could be measured. We also estimate the double longitudinal spin asymmetry ALL of J/ψ production using a spectator model result for g1Lg(x,pT2).
@article{arxiv.2310.00609,
title = {Gluon TMDs from J/$\psi$ production in longitudinally polarized deeply inelastic scattering},
author = {Huachao liu and Xiupeng xie and Zhun Lu},
journal= {arXiv preprint arXiv:2310.00609},
year = {2023}
}