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Recently it has been put forward that linearly polarized gluons insideunpolarized protons affect the transverse momentum distribution of final stateparticles in hadronic collisions. They lead to a characteristic modulation ofthe differential cross section in Higgs production and to azimuthal asymmetriesin, for instance, heavy quark pair production. Here we study the effect oncharmonium and bottomonium production in hadronic collisions, such as at LHCband at the proposed fixed target experiment AFTER at LHC. We focus mainly onthe scalar and pseudoscalar quarkonia, eta_c, chi_{c0}, eta_b, chi_{b0}, whichallow for an angular independent investigation. Within the framework oftransverse momentum dependent factorization in combination with thenonrelativistic QCD based color-singlet quarkonium model, we show for smalltransverse momentum (q_T^2 \ll 4 M_Q^2) that the scalar and pseudoscalarquarkonium production cross sections are modified in different ways by linearlypolarized gluons, while their effects on the production of higher angularmomentum quarkonium states are strongly suppressed. Comparisons to chi_{c2},chi_{b2} production can help to cancel out uncertainties. Together with theanalogous study in Higgs production at LHC, quarkonium production can moreoverbe used to test the scale dependence of the linearly polarized gluondistribution over a large energy range.

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER