Incoherent ${\rm J}/\psi$ production at large $|t|$ identifies the onset of saturation at the LHC

We predict that the onset of gluon saturation can be uniquely identified using incoherent ${\rm J}/\psi$ production in Pb$\unicode{x2013}$Pb collisions at currently accessible energies of the LHC. The diffractive incoherent photo-production of a ${\rm J}/\psi$ vector meson off a hadron provides information on the partonic structure of the hadron. Within the Good-Walker approach it specifically measures the variance over possible target configurations of the hadronic colour field. For this process then, gluon saturation sets in when the cross section reaches a maximum, as a function of the centre-of-mass energy of the photon-hadron system ($W$), and then decreases. We benchmark the energy-dependent hot-spot model against data from HERA and the LHC and demonstrate a good description of the available data. We show that the study of the energy dependence of the incoherent production of ${\rm J}/\psi$ allows us to pinpoint the onset of saturation effects by selecting the region of Mandelstam-$t$ around 1 GeV$^2$ where the contribution of hot spots is dominant. We predict the onset of saturation in a Pb target to occur for $W$ around a few hundred GeV. This can be measured with current data in ultra-peripheral Pb$\unicode{x2013}$Pb collisions at the LHC.