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We study the exclusive diffractive $c \bar c$ photoproduction inultraperipheral $pA$ collisions. The formalism makes use of off-diagonalgeneralizations of the unintegrated gluon distribution, the so-calledgeneralized transverse momentum dependent distributions (GTMDs). We present twodifferent formulations. The first one is based directly on gluon GTMDparametrizations in momentum space. Another option is the calculation of theGTMD as a Fourier transform of the dipole-nucleon scattering amplitude$N(Y,\vec{r}_{\perp},\vec{b}_{\perp})$. The latter approach requires some extraregularization discussed in the paper. Different dipole amplitudes from theliterature are used. Compared to previous calculations in the literature, weintegrate over the full phase space and therefore cross sections for realisticconditions are obtained. We present distributions in rapidity of $c$ or $\barc$, transverse momentum of the $c \bar c$ pair, four-momentum transfer squaredas well as the azimuthal correlation between a sum and a difference of the $c$and $\bar c$ transverse momenta. The azimuthal correlations are partially dueto the so-called elliptic gluon Wigner distribution. Different models lead todifferent modulations in the azimuthal angle. The modulations are generallysmaller than 5%. They depend on the range of transverse momentum selected forthe calculation.

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