1 Introduction

Photonuclear reactions can be studied in ultra-peripheral collisions (UPCs) of heavy ions where the two nuclei pass by with an impact parameter larger than the sum of their radii. Hadronic interactions are suppressed and the dominant electromagnetic interactions are mediated by photons of small virtualities. The intensity of the photon flux is growing with the squared nuclear charge of the colliding ion resulting in large cross sections for the photoproduction of vector mesons in heavy-ion collisions. The photoproduction process has a clear experimental signature: the decay products of vector mesons are the only signal in an otherwise empty detector.

The physics of vector meson photoproduction is described in [1,2,3,4]. Photoproduction of vector mesons in ion collisions can either be coherent, i.e. the photon interacts consistently with all nucleons in a nucleus, or incoherent, i.e. the photon interacts with a single nucleon. Experimentally, one can distinguish between these two production types through the typical transverse momentum of the produced vector mesons, which is inversely proportional to the transverse size of the target. While the coherent photoproduction is characterized by the production of mesons with low transverse momentum (\(\langle p_{\mathrm{T}} \rangle \sim \) 60 MeV/c), the incoherent is dominated by mesons with higher values (\(\langle p_{\mathrm{T}} \rangle \sim \) 500 MeV/c). In the first case, the nuclei usually do not dissociate, but the electromagnetic fields of ultrarelativistic heavy nuclei are strong enough to develop other independent soft electromagnetic interactions accompanying the coherent photoproduction process and resulting in the excitation of one or both of the nuclei. In the second case, the nucleus breaks up and usually emits neutrons close to the beam rapidities which can be measured in zero-degree calorimeters (ZDC) placed at long distances on both sides of the detector [5]. The incoherent photoproduction can also be accompanied by the excitation and dissociation of the target nucleon resulting in even higher transverse momenta of the produced vector mesons [6].

Coherent heavy vector meson photoproduction is of particular interest because of its connection with the gluon distribution functions (PDFs) in protons and nuclei [7]. At low Bjorken-x values, nuclear parton distribution functions are significantly suppressed in the nucleus with respect to free proton PDFs, a phenomenon known as parton shadowing [8]. Shadowing effects are usually attributed to multiple scattering and addressed in various phenomenological approaches based on elastic Glauber-like rescatterings of hadronic components of the photon, Glauber–Gribov inelastic rescatterings, and high-density QCD [9,10,