Quarkonium Polarization and the Long Distance Matrix Elements Hierarchies using Jet Substructure

TL;DR

This paper studies quarkonium production in jets at the LHC using the FJF approach, revealing how jet energy dependence can indicate dominant production channels and inform polarization properties.

Contribution

It introduces a method to determine the dominant NRQCD production channel for $J/\psi$ in jets based on energy dependence, extending previous predictions to cross sections.

Findings

Depolarizing $^1S_0^{[8]}$ channel dominates at high $z$ and jet energy.

Normalized cross section decreases with jet energy for $z > 0.5$, indicating channel dominance.

Comparison of long distance matrix elements from different groups provides insights into polarization.

Abstract

We investigate the quarkonium production mechanisms in jets at the LHC, using the Fragmenting Jet Functions (FJF) approach. Specifically, we discuss the jet energy dependence of the $J/\psi$ production cross section at the LHC. By comparing the cross sections for the different NRQCD production channels ($^1S_0^{[8]}$,$^3S_1^{[8]}$,$^3P_J^{[8]}$, and $^3S_1^{[1]}$), we find that at fixed values of energy fraction $z$ carried by the $J/\psi$, if the normalized cross section is a decreasing function of the jet energy, in particular for $z > 0.5$, then the depolarizing $^1S_0^{[8]}$ must be the dominant channel. This makes the prediction made in [Baumgart et al., JHEP 1411, 003 (2014)] for the FJF's also true for the cross section. We also make comparisons between the long distance matrix elements extracted by various groups. This analysis could potentially shed light on the polarization properties of the $J/\psi$ production in high $p_T$ region.