Polarized TMD fragmentation functions for $J/\psi$ production

We calculate the matching, at leading order, of the transverse momentum dependent fragmentation functions (TMDFFs) for light quarks and gluons fragmenting to a $J/\psi$ onto polarized non-relativistic QCD (NRQCD) TMDFFs. The NRQCD TMDFFs have an operator-product-expansion in terms of non-perturbative NRQCD production matrix elements. Using the results we obtain, we make predictions for the light quark fragmentation contribution to the production of polarized $J/\psi$ in semi-inclusive deep inelastic scattering (SIDIS) both for unpolarized and longitudinally polarized beams. These results are an important contribution to polarized $J/\psi$ production in SIDIS, and thus are needed for comparison with experiments at the future Electron-Ion Collider.