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

We investigate the proposal that the rise with energy of the ratio of the exclusive photoproduction cross sections of vector mesons $\Psi \left(2s\right)$ and $J/\Psi$ can serve as an indicator for the presence of high gluon densities and associated nonlinear 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 nonlinear (Balitsky-Kovchegov) evolution equations, the current study is based on the Golec-Biernat Wüsthoff and Bartels Golec-Biernat Kowalski models, which allows us to assess more directly the relevance of nonlinear 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 $\Psi \left(2s\right)$ wave function and only manifests itself for the complete nonlinear 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 $\Psi \left(2s\right)$ and $J/\Psi$ photoproduction cross sections for both scattering on a proton and a lead nucleus.