Polarized TMD fragmentation functions for J/ψ production

We calculate the matching, at leading order, of the transverse momentum-dependent fragmentation functions (TMDFFs) for light quarks and gluons fragmenting to a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi></a:math> onto polarized nonrelativistic QCD (NRQCD) TMDFFs. The NRQCD TMDFFs have an operator product expansion in terms of nonperturbative NRQCD production matrix elements. Using the results we obtain, we make predictions for the light quark fragmentation contribution to the production of polarized <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi></c:math> in semi-inclusive deep inelastic scattering (SIDIS) both for unpolarized and longitudinally polarized beams. These results are an important contribution to polarized <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi>ψ</e:mi></e:math> production in SIDIS and thus are needed for comparison with experiments at the future Electron-Ion Collider.