Incoherent J/ψ production at large |t| identifies the onset of saturation at the LHC

The study of incoherent production of a vector meson in diffractive processes provides information about the inner composition of the target hadron at the partonic level. The incoherent cross section is sensitivite to fluctuations in the configuration of the color field of the target. The energy-dependent hot-spot model, based on the color dipole approach, incorporates subnucleon degrees of freedom known as hot spots. These hot spots represent regions of high gluonic density, and their positions fluctuate event-by-event. As the collision energy increases, an intense concentration of gluons within hadrons occurs, leading to a transition from a dilute to a saturated regime. To investigate this phenomenon, we propose studying the energy dependance of incoherent photo-production of vector mesons in diffractive processes at various values of the Mandelstam-$t$ variable. The $|t|$ distribution is related to fluctuations of different transverse sizes. The coherent cross section is sensitive to nuclear sizes, while incoherent processes are sensitive to both nucleon and hot spot sizes. We predict that the onset of saturation can be determined at the LHC by measuring the energy dependence of the incoherent $\rm{J}/\psi$ photo-production cross section at large $|t|$, a region dominated by hot spot contributions.