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Linearly polarized gluon effects in unpolarized collisions

Linear polarization of gluons inside unpolarized hadrons affects the transverse momentum distribution of produced spin-0 particles, such as of the Higgs or (pseudo-)scalar quarkonium states at LHC. Despite the currently unknown amount of linear gluon polarization, a range of predictions can be obtained, using TMD evolution, which indicates that their effect is on the few percent level in Higgs production, but can be much larger in quarkonium production. Together with asymmetries in open charm or bottom production in electro-production at an Electron-Ion Collider, the size and sign of the linear gluon polarization could be extracted experimentally. These processes also allow to test the behavior expected at small $x$ in and outside the saturation region.