Probing proton structure with $c \bar c$ correlations in ultraperipheral $pA$ collisions

We study the exclusive diffractive $c \bar c$ photoproduction in ultraperipheral $pA$ collisions. The formalism makes use of off-diagonal generalizations of the unintegrated gluon distribution, the so-called generalized transverse momentum dependent distributions (GTMDs). We present two different formulations. The first one is based directly on gluon GTMD parametrizations in momentum space. Another option is the calculation of the GTMD as a Fourier transform of the dipole-nucleon scattering amplitude $N(Y,\vec{r}_{\perp},\vec{b}_{\perp})$. The latter approach requires some extra regularization discussed in the paper. Different dipole amplitudes from the literature are used. Compared to previous calculations in the literature, we integrate over the full phase space and therefore cross sections for realistic conditions are obtained. We present distributions in rapidity of $c$ or $\bar c$, transverse momentum of the $c \bar c$ pair, four-momentum transfer squared as well as the azimuthal correlation between a sum and a difference of the $c$ and $\bar c$ transverse momenta. The azimuthal correlations are partially due to the so-called elliptic gluon Wigner distribution. Different models lead to different modulations in the azimuthal angle. The modulations are generally smaller than 5%. They depend on the range of transverse momentum selected for the calculation.