A global analysis of ATLAS and CMS measurements reveals a startling observation: the directly-produced mid-rapidity J/ψ, ψ(2S), χc1, χc2 and Υ(nS) have differential cross sections of seemingly identical shapes, when presented as a function of the mass-rescaled transverse momentum, pT/M. This universal momentum scaling pattern, together with the absence of strong polarizations of S-wave mesons (directly or indirectly produced), strongly suggests that the QQbar production mechanisms do not depend on the quantum numbers and mass of the final quarkonium state.
The remarkable similarity of kinematic behaviours among S- and P-wave quarkonia is not a natural expectation of non-relativistic QCD (NRQCD), where each quarkonium state is expected to reflect a specific family of elementary production processes, of significantly different pT-differential cross sections. Remarkably, accurate kinematic cancellations among the variegated (singlet and octet) NRQCD terms can lead to a surprisingly good description of the data.
This peculiar tuning of the NRQCD mixtures leads to a clear prediction regarding the χc1 and χc2 polarizations, the only observables not yet measured: they should be almost maximally different from one another, and from the J/ψ polarization, a striking exception in the global panorama of quarkonium production. Measurements of the difference between the χc1, χc2 and J/ψ polarizations, complementing the observed identity of momentum dependences, represent a decisive probe of NRQCD.
Moreover, the application of dimensional analysis to LHC data (Drell--Yan and quarkonium cross sections) provides strong experimental evidence supporting the validity of the factorization ansatz, a cornerstone of NRQCD. Furthermore, 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.