Linearly polarized gluons in charmonium and bottomonium production in the color octet model

We study the possibility of probing the unpolarized and linearly polarized transverse momentum-dependent gluon distributions in unpolarized pp collision in charmonium and bottomonium production, employing the nonrelativistic QCD-based color octet model within transverse momentum-dependent factorization framework. The transverse momentum (p(T)) and rapidity distributions of J/psi and gamma(1S) at the LHCb, Relativistic Heavy Ion Collider (RHIC), and A Fixed Target Experiment (AFTER) energies are estimated. Significant modulations in the transverse-momentum spectrum of quarkonium in the low-p(T) region are obtained when contributions of linearly polarized gluons inside an unpolarized proton are taken into account. The results of quarkonium production in the color octet model and color evaporation model are compared.