  The observation of unpolarized quarkonium production in high energy pp
collisions, at mid rapidity, implies a significant violation of the
non-relativistic QCD (NRQCD) velocity scaling rules. A precise experimental
confirmation of this picture could definitely rule out the current formulation
of the factorization expansion. This conclusion relies on current perturbative
determinations of the short-distance kinematic factors and may be reverted if
improved calculations would modify, in a very specific way, their transverse
momentum dependences. That solution would result, however, in a full degeneracy
in the presently assumed basis of $^{2S+1}L_J$ Fock states. Therefore, whatever
the outcome, improved polarization measurements will challenge and improve our
fundamental understanding of quarkonium production.
