^{1}

^{*}

^{2}

^{†}

Corresponding author: agnieszka.luszczak@desy.de

wolfgang.schafer@ifj.edu.pl

^{3}.

We investigate the exclusive photoproduction of

Following the early theoretical work

The production of vector mesons composed of heavy quarks, such as the

Much attention has been paid in the past on diffractive photo- and electroproduction of vector mesons on the proton. A large body of data has been accumulated at the German Electron Synchrotron-Hadron-Electron Ring Accelerator (DESY-HERA) facility. For a review of experimental data and of the theoretical approaches, see Ref.

Here, we discuss the coherent diffractive photoproduction in the same approach which we used earlier for the incoherent photoproduction of

Let us start with a brief review of the formalism for production of a vector mesons ^{1}

A form of the phase which does not vanish at

The real part of the amplitude is restored from analyticity from the

When it comes to nuclear targets, one should realize that color dipoles can be regarded as eigenstates of the interaction, and one can apply the standard rules of Glauber theory

Coherent photoproduction of a vector meson in which the nucleus stays in its ground state.

The dipole amplitude of Eq.

In the dipole picture, the deep inelastic scattering is viewed as a two-stage process; first the virtual photon fluctuates into a dipole, which consists of a quark-antiquark pair (or a

The scattering amplitude is a product of the virtual photon wave-function

Numerous models for the dipole cross section have been developed to test various aspects of the data. In the following, we will shortly review some of them, which have been obtained from fitting data on the inclusive proton structure function and which we will test against the

We will use three different dipole models, all of which have been fitted to structure function data including charm. They differ in the treatment of the underlying QCD dynamics: the Golec-Biernat-Wüsthoff (GBW) parametrization is the most phenomenological one and rests on a geometric scaling form where the dipole cross section depends only on the variable

The dipole model became a popular tool in investigations of deep-inelastic scattering following the observation of Golec-Biernat and Wüsthoff

In the GBW model, the dipole-proton cross-section

The GBW model provided a good description of data from medium

In this paper, we use a new fit of the GBW form of the dipole cross section obtained by Golec-Biernat and Sapeta in Ref.

The evolution ansatz of the GBW model was improved in the model proposed by Bartels, Golec-Biernat, and Kowalski (BGK)

The gluon density, which is parametrized at the starting scale

The free parameters for this model are

BGK fit with fitted valence quarks for

Another parametrization of the dipole cross section which gives the latter in a simple analytic form is the IIM model

Let us now turn to the numerical results we obtained for the total exclusive photoproduction cross section of

Total cross section for the exclusive photoproduction

We now turn to our results for ultraperipheral heavy-ion collisions. We obtain the rapidity-dependent cross section for exclusive

Exclusive photoproduction in ultraperipheral heavy-ion collisions.

We use the standard form of the Weizsäcker-Williams flux (see, e.g., the reviews

In order to understand the kinematics a bit better, in Tables

Subenergies

Subenergies

In Fig.

In Fig.

The overall picture suggests that the Glauber-Gribov formalism in the color dipole approach works reasonably well at not too high energies (or not too small

This point is also borne out by Fig.

We see that at high energies we overestimate the data. However even at the highest energy

In fact, in our calculations, we included only the rescattering of the

It is well understood that at small

One may ask finally if the light-cone wave function can be the scapegoat. Indeed, in a careful analysis of some theoretical uncertainties

A different approach has recently been taken in Ref.

Rapidity-dependent cross-section

Rapidity-dependent cross-section

Rapidity-dependent cross-section

The total cross-section

In this paper, we have presented calculations using the Glauber-Gribov theory for coherent exclusive photoproduction of

We have applied our results to the exclusive

The color dipoles play the role of the eigenstates of the scattering matrix and take into account the inelastic shadowing corrections. We have taken into account the rescattering of a

Although there is substantial uncertainty as to how to include the skewedness correction in to the nuclear amplitude, the description of published and preliminary data can be regarded satisfactory. However, the data point taken by the ALICE Collaboration at midrapidity for

We believe that explicit account of higher Fock states is necessary in this kinematic region. This is consistent with an analysis of nuclear shadowing and deep inelastic diffraction on nuclei in Ref.

Whether the correct approach is a resummation of their effect in a BFKL-BK framework, or whether they can be absorbed into a leading-twist shadowing of the collinear nuclear glue is an open issue. It stands to reason that this issue can hardly be resolved by only one observable, measured essentially at one hard scale, and that future measurements at an electron-ion collider will be crucial for a deeper understanding of the nuclear glue.

This work was partially supported by the Polish National Science Center Grant No. DEC-2014/15/B/ST2/02528.