From identical S- and P-wave pT/M spectra to maximally distinct polarizations: probing NRQCD with chi states

TL;DR

This paper analyzes quarkonium production data, revealing unexpected similarities in kinematic distributions among different states, and predicts distinct polarization patterns that can test the validity of NRQCD models.

Contribution

It demonstrates how NRQCD can produce similar kinematic behaviors across different quarkonium states and predicts unique polarization differences as a critical test.

Findings

Kinematic distributions of different quarkonia are nearly identical.

NRQCD's complex term cancellations can explain data.

Predicted polarization differences between states are maximally distinct.

Abstract

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, $p_{\rm T}/M$. 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 $p_{\rm T}$-differential cross sections. Remarkably, accurate kinematic cancellations among the variegated 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.