Nucleon dissociation and incoherent $J/\psi$ photoproduction on nuclei in ion ultraperipheral collisions at the CERN Large Hadron Collider

Using the general notion of cross section fluctuations in hadron--nucleus scattering at high energies, we derive an expression for the cross section of incoherent $J/\psi$ photoproduction on heavy nuclei $d\sigma_{\gamma A \to J/\psi Y}/dt$, which includes both elastic $d\sigma_{\gamma p \to J/\psi p}/dt$ and proton-dissociation $d\sigma_{\gamma p \to J/\psi Y}/dt$ photoproduction on target nucleons. We find that with good accuracy, $d\sigma_{\gamma A \to J/\psi Y}/dt$ can be expressed as a product of the sum of the $d\sigma_{\gamma p \to J/\psi p}/dt$ and $d\sigma_{\gamma p \to J/\psi Y}/dt$ cross sections, which have been measured at HERA, and the common nuclear shadowing factor, which is calculated using the leading twist nuclear shadowing model. Our prediction for the cross section of incoherent $J/\psi$ photoproduction in Pb-Pb UPCs at $\sqrt{s_{NN}}=2.76$ TeV and $y=0$, $d\sigma_{AA \to J/\psi AY}(y=0)/dy=0.59-1.24$ mb, agrees within significant theoretical uncertainties with the data of the ALICE collaboration.