# NRQCD colour-octet expansion vs LHC quarkonium production: signs of a hierarchy puzzle?

## TL;DR

This paper discusses how recent experimental results on quarkonium production challenge the NRQCD velocity scaling rules and the factorization approach, highlighting the need for improved measurements to clarify the underlying production mechanisms.

## Contribution

It critically examines the discrepancies between NRQCD predictions and experimental data, emphasizing the potential hierarchy puzzle and the importance of polarization measurements.

## Key findings

- Unpolarized quarkonium production violates NRQCD velocity scaling rules.
- Current perturbative calculations may be insufficient to explain data.
- Improved polarization measurements are essential for understanding quarkonium production.

## Abstract

The observation of unpolarized quarkonium production in high energy pp collisions, at mid rapidity, implies a significant violation of the non-relativistic QCD (NRQCD) velocity scaling rules. A precise experimental confirmation of this picture could definitely rule out the current formulation of the factorization expansion. This conclusion relies on current perturbative determinations of the short-distance kinematic factors and may be reverted if improved calculations would modify, in a very specific way, their transverse momentum dependences. That solution would result, however, in a full degeneracy in the presently assumed basis of $^{2S+1}L_J$ Fock states. Therefore, whatever the outcome, improved polarization measurements will challenge and improve our fundamental understanding of quarkonium production.