Towards the experimental clarification of quarkonium polarization

TL;DR

This paper emphasizes the importance of proper analysis methods in quarkonium polarization studies, introduces a frame-invariant formalism to improve measurement accuracy, and aims to resolve existing experimental-theoretical discrepancies.

Contribution

It introduces a frame-invariant formalism for quarkonium polarization analysis that reduces experimental biases and enhances comparison with theoretical models.

Findings

Proposes a frame-invariant formalism based on rotational invariance.

Highlights the impact of reference frame choice on polarization measurements.

Suggests that the new approach will accelerate understanding of quarkonium production.

Abstract

We highlight issues which are often underestimated in the experimental analyses on quarkonium polarization: the relation between the parameters of the angular distributions and the angular momentum composition of the quarkonium, the importance of the choice of the reference frame, the interplay between observed decay and production kinematics, and the consequent influence of the experimental acceptance on the comparison between experimental measurements and theoretical calculations. Given the puzzles raised by the available experimental results, new measurements must provide more detailed information, such that physical conclusions can be derived without relying on model-dependent assumptions. We describe a frame-invariant formalism which minimizes the dependence of the measurements on the experimental acceptance, facilitates the comparison with theoretical calculations, and probes systematic effects due to experimental biases. This formalism is a direct and generic consequence of the rotational invariance of the dilepton decay distribution and is independent of any assumptions specific to particular models of quarkonium production. The use of this improved approach, which exploits the intrinsic multidimensionality of the problem, will significantly contribute to a faster progress in our understanding of quarkonium production, especially if adopted as a common analysis framework by the LHC experiments, which will soon perform analyses of quarkonium polarization in proton-proton collisions.