  While non-relativistic QCD (NRQCD) foresees a variety of elementary
quarkonium production mechanisms naturally leading to state-dependent kinematic
patterns, the LHC cross sections and polarization measurements reveal a
remarkably simple production scenario, independent of the quantum numbers and
masses of the quarkonia. Surprisingly, NRQCD is able to accommodate the
observed universal scenario, through a series of conspiring cancellations
smoothing out its otherwise variegated hierarchy of mechanisms. This seemingly
unnatural solution implies that the $\chi_{c1}$ and $\chi_{c2}$ polarizations,
not yet measured, are strong and opposite, representing the only potential
exception to a remarkably simple picture of quarkonium production. The
observation of a large difference between $\chi_{c2}$ and $\chi_{c1}$
polarizations, which cannot be indirectly extracted from existing measurements
because they mutually cancel each other in their contribution to the observed
J/$\psi$ production, would be a smoking gun signal finally proving the
multifaceted but mysteriously elusive structure of NRQCD. On the other hand,
the measurement of two similar, small polarizations will urge improved P-wave
calculations, if not a substantial revision of the NRQCD hierarchies.
