Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Recently it has been put forward that linearly polarized gluons inside unpolarized protons affect the transverse momentum distribution of final state particles in hadronic collisions. They lead to a characteristic modulation of the differential cross section in Higgs production and to azimuthal asymmetries in, for instance, heavy quark pair production. Here we study the effect on charmonium and bottomonium production in hadronic collisions, such as at LHCb and at the proposed fixed target experiment AFTER at LHC. We focus mainly on the scalar and pseudoscalar quarkonia, eta(c), chi(c0), eta(b), chi(b0), which allow for an angular independent investigation. Within the framework of transverse momentum dependent factorization in combination with the nonrelativistic QCD based color-singlet quarkonium model, we show for small transverse momentum (q(T)(2) << 4M(Q)(2)) that the scalar and pseudoscalar quarkonium production cross sections are modified in different ways by linearly polarized gluons, while their effects on the production of higher angular momentum quarkonium states are strongly suppressed. Comparisons to chi(c2), chi(b2) production can help to cancel out uncertainties. Together with the analogous study in Higgs production at LHC, quarkonium production can moreover be used to test the scale dependence of the linearly polarized gluon distribution over a large energy range.