Ratio of $J/\Psi$ and $\Psi(2s)$ exclusive photoproduction cross-sections as an indicator for the presence of non-linear QCD evolution

TL;DR

This paper explores how the energy-dependent ratio of $$ and $$ vector meson photoproduction cross-sections can indicate non-linear QCD effects, using models that incorporate gluon saturation and comparing with experimental data.

Contribution

It demonstrates that the energy rise of the ratio is linked to non-linear QCD dynamics and the node in the $$ wave function, providing predictions for proton and nuclear targets.

Findings

The ratio's rise is only present in non-linear models.

Linear models fail to reproduce the ratio increase.

Predictions align with recent ALICE data.

Abstract

We investigate the proposal that the rise with energy of the ratio of the exclusive photo-production cross-sections of vector mesons $\Psi(2s)$ and $J/\Psi$ can serve as an indicator for the presence of high gluon densities and associated non-linear high energy evolution; we study this proposal for both photoproduction on a proton and a lead nucleus. While previous studies were based on unintegrated gluon distributions subject to linear (Balitsky-Fadin-Kuraev-Lipatov) and non-linear (Balitsky-Kovchegov) evolution equations, the current study is based on the Golec-Biernat W\"usthoff (GBW) and Bartels Golec-Biernat Kowalski (BGK) models, which allow assessing more directly the relevance of non-linear corrections for the description of the energy dependence of the photoproduction cross-section. We find that the rise of the ratio is directly related to the presence of a node in the $\Psi(2s)$ wave function and only manifests itself for the complete non-linear models, while it is absent for their linearized versions. We further provide predictions based on leading order collinear factorization and examine to which extent such an approach can mimic a ratio rising with energy. We also provide a description of recent ALICE data on the energy dependence of the photonuclear $J/\Psi$ production cross-section and give predictions for the energy dependence of the ratio of $\Psi(2s)$ and $J/\Psi$ photoproduction cross-sections for both scattering on a proton and a lead nucleus.