# Signs for the onset of gluon saturation in exclusive photo-production of vector mesons

## TL;DR

This paper analyzes the energy dependence of vector meson photo-production cross-sections to identify signs of gluon saturation, finding that non-linear QCD effects are essential for accurate data description at high energies.

## Contribution

It demonstrates that incorporating non-linear gluon evolution models is crucial to explain high-energy vector meson production, indicating the onset of gluon saturation in low x proton.

## Key findings

- Linear NLO BFKL evolution fails at high energies without large corrections.
- Non-linear corrections enable accurate description of J/Ψ data.
- Evidence suggests high gluon densities indicating gluon saturation.

## Abstract

We investigate the energy dependence of the photo-production cross-section of vector mesons $J/\Psi$ and $\Upsilon$, measured by both HERA experiments H1 and ZEUS in electron-proton collisions and by LHC experiments ALICE, CMS and LHCb in ultra-peripheral proton-proton and ultra-peripheral proton-lead collisions. Our study uses 2 particular fits of inclusive unintegrated gluon distribution, based on non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution (Hentschinski-Sabio Vera-Salas gluon; HSS). We find that linear next-to-leading order BFKL evolution can only describe production at highest energies, if perturbative corrections are increased to unnaturally large values; rendering this corrections small, the growth with energy is too strong in the LHC region and the description of $J/\Psi$ data fails. For the KS gluon we find that an accurate description of $J/\Psi$ data is possible if non-linear corrections to low x QCD evolution are taken into account; without such correction a description of data fails. We interpret this observation as a clear signal for the presence of high gluon densities in low x the proton, characteristic for the onset of gluon saturation.