From identical S- and P-wave $$p_\mathrm{T}$$ pT spectra to maximally distinct polarizations: probing NRQCD with $$\chi $$ χ states

Abstract

Abstract A global analysis of ATLAS and CMS measurements reveals that, at mid-rapidity, the directly-produced $$\chi _{c1}$$ χc1 , $$\chi _{c2}$$ χc2 and J/$$\psi $$ ψ mesons have differential cross sections of seemingly identical shapes, when presented as a function of the mass-rescaled transverse momentum, $$p_\mathrm{T}/M$$ pT/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 $$p_\mathrm{T}$$ pT -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 $$\chi _{c1}$$ χc1 and $$\chi _{c2}$$ χc2 polarizations, the only observables not yet measured: they should be almost maximally different from one another, and from the J/$$\psi $$ ψ polarization, a striking exception in the global panorama of quarkonium production. Measurements of the difference between the $$\chi _{c1}$$ χc1 , $$\chi _{c2}$$ χc2 and J/$$\psi $$ ψ polarizations, complementing the observed identity of momentum dependences, represent a decisive probe of NRQCD.