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Polarization measurements are the best instrument to understand how quark andantiquark combine into the different quarkonium states, but no model has so farsucceeded in explaining the measured J/psi and Upsilon polarizations. On theother hand, the experimental data in proton-antiproton and proton-nucleuscollisions are inconsistent, incomplete and ambiguous. New analyses will haveto properly address often underestimated issues: the existence of azimuthalanisotropies, the dependence on the reference frame, the influence of theexperimental acceptance on the comparison with other measurements and withtheory. Additionally, a recently developed frame-invariant formalism willprovide an alternative and often more immediate physical viewpoint and, at thesame time, will help probing systematic effects due to experimental biases. Therole of feed-down decays from heavier states, a crucial missing piece in thecurrent experimental knowledge, will have to be investigated. Ultimately,quarkonium polarization measurements will also offer new possibilities in thestudy of the properties of the quark-gluon plasma.

Questions and prospects in quarkonium polarization measurements from proton-proton to nucleus-nucleus collisions