Energy dependence of dissociative $\mathrm{J}\mathrm{/}\psi$ photoproduction as a signature of gluon saturation at the LHC

We have developed a model in which the quantum fluctuations of the proton structure are characterised by hot spots, whose number grows with decreasing Bjorken-$x$. Our model reproduces the $F_2(x,Q^2)$ data from HERA at the relevant scale, as well as the exclusive and dissociative $\mathrm{J}\mathrm{/}\psi$ photoproduction data from H1 and ALICE. Our model predicts that for $W_{\gamma \mathrm{p}}\approx 500$ GeV, the dissociative $\mathrm{J}\mathrm{/}\psi$ cross section reaches a maximum and then decreases steeply with energy, which is in qualitatively good agreement to a recent observation that the dissociative $\mathrm{J}\mathrm{/}\psi$ background in the exclusive $\mathrm{J}\mathrm{/}\psi$ sample measured in photoproduction by ALICE decreases as energy increases. Our prediction provides a clear signature for gluon saturation at LHC energies.