  Dimensional analysis reveals general kinematic scaling rules for the
momentum, mass, and energy dependence of Drell-Yan and quarkonium cross
sections. Their application to mid-rapidity LHC data provides strong
experimental evidence supporting the validity of the factorization ansatz, a
cornerstone of non-relativistic QCD, still lacking theoretical demonstration.
Moreover, data-driven patterns emerge for the factorizable long-distance
bound-state formation effects, including a remarkable correlation between the
S-wave quarkonium cross sections and their binding energies. Assuming that this
scaling can be extended to the P-wave case, we obtain precise predictions for
the not yet measured feed-down fractions, thereby providing a complete picture
of the charmonium and bottomonium feed-down structure. This is crucial
information for quantitative interpretations of quarkonium production data,
including studies of the suppression patterns measured in nucleus-nucleus
collisions.
