  We highlight issues which are often underestimated in the experimental
analyses on quarkonium polarization: the relation between the parameters of the
angular distributions and the angular momentum composition of the quarkonium,
the importance of the choice of the reference frame, the interplay between
observed decay and production kinematics, and the consequent influence of the
experimental acceptance on the comparison between experimental measurements and
theoretical calculations. Given the puzzles raised by the available
experimental results, new measurements must provide more detailed information,
such that physical conclusions can be derived without relying on
model-dependent assumptions. We describe a frame-invariant formalism which
minimizes the dependence of the measurements on the experimental acceptance,
facilitates the comparison with theoretical calculations, and probes systematic
effects due to experimental biases. This formalism is a direct and generic
consequence of the rotational invariance of the dilepton decay distribution and
is independent of any assumptions specific to particular models of quarkonium
production. The use of this improved approach, which exploits the intrinsic
multidimensionality of the problem, will significantly contribute to a faster
progress in our understanding of quarkonium production, especially if adopted
as a common analysis framework by the LHC experiments, which will soon perform
analyses of quarkonium polarization in proton-proton collisions.
