From identical S- and P-wave p T spectra to maximally distinct polarizations: probing NRQCD with χ states

A global analysis of ATLAS and CMS measurements reveals that, at mid-rapidity, the directly-produced ${\chi }_{c1}$ , ${\chi }_{c2}$ and J/ $\psi$ mesons have differential cross sections of seemingly identical shapes, when presented as a function of the mass-rescaled transverse momentum, $p_T/M$ . This identity of kinematic behaviours among S- and P-wave quarkonia is certainly not a natural expectation of non-relativistic QCD (NRQCD), where each quarkonium state is supposed to reflect a specific family of elementary production processes, of significantly different $p_T$ -differential cross sections. Remarkably, accurate kinematic cancellations among the various NRQCD terms (colour singlets and octets) of its factorization expansion can lead to a surprisingly good description of the data. This peculiar tuning of the NRQCD mixtures leads to a clear prediction regarding the ${\chi }_{c1}$ and ${\chi }_{c2}$ polarizations, the only observables not yet measured: they should be almost maximally different from one another, and from the J/ $\psi$ polarization, a striking exception in the global panorama of quarkonium production. Measurements of the difference between the ${\chi }_{c1}$ , ${\chi }_{c2}$ and J/ $\psi$ polarizations, complementing the observed identity of momentum dependences, represent a decisive probe of NRQCD.