NRQCD colour-octet expansion vs LHC quarkonium production: signs of a hierarchy puzzle?

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.