Quarkonium polarization in low-$p_{\rm T}$ hadro-production: from past data to future opportunities

TL;DR

This paper analyzes diverse experimental data on quarkonium polarization, proposing a simple physical interpretation based on production mechanisms, and offers predictions for future experiments to test and refine understanding of parton distributions.

Contribution

It introduces a unified interpretation of quarkonium polarization data based on gluon-gluon fusion and quark-antiquark annihilation, and provides testable predictions for future experiments.

Findings

Qualitative patterns support the production mechanism hypothesis.

Quantitative description of polarization in specific kinematic domain.

Predictions for future measurements to constrain pion parton distributions.

Abstract

Several fixed-target experiments reported J/$\psi$ and $\Upsilon$ polarization measurements, as functions of Feynman $x$ ($x_{\rm F}$) and transverse momentum ($p_{\rm T}$), in three different polarization frames, using different combinations of beam particles, target nuclei and collision energies. The data form such a diverse and heterogeneous picture that, at first sight, no clear trends can be observed. A more detailed look, however, allows us to discern qualitative physical patterns that inspire and support a simple interpretation: the directly-produced quarkonia result from either gluon-gluon fusion or from quark-antiquark annihilation, with the former mesons being fully longitudinally polarized and the latter being fully transversely polarized. This hypothesis provides a reasonable quantitative description of the J/$\psi$ and $\Upsilon$(1S) polarizations measured in the $x_{\rm F} \lesssim 0.5$ kinematical domain. We provide predictions that can be experimentally tested, using proton and/or pion beams, and show that improved J/$\psi$ and $\psi$(2S) polarization measurements in pion-nucleus collisions can provide significant constraints on the poorly known parton distribution functions of the pion.