Low-pT quarkonium polarization measurements: Challenges and opportunities

Several fixed-target experiments reported J/ψ and ϒ polarizations, as functions of Feynman x (xF) and transverse momentum (PT), in three different frames, using different combinations of beam particles, target nuclei, and collision energies. Despite the diverse and heterogeneous picture formed by these measurements, a detailed look allows us to discern qualitative physical patterns that inspire a simple empirical model. This data-driven scenario offers a good quantitative description of the J/ψ and ϒ(1S) polarizations measured in proton- and pion-nucleus collisions, in the xF 0.5 domain: more than 80 data points (not statistically independent) are well reproduced with only one free parameter. This study sets the context for future low-PT quarkonium polarization measurements in proton- and pion-nucleus collisions, such as those to be made by the AMBER experiment, and shows that such measurements provide significant constraints on the poorly-known parton distribution functions of the pion.