DPS mechanism for associated $cbar{c} l^+l^-$ production in $AA$ UPCs as a probe for photon density inside the nucleus

We discuss the associated $cbar{c}$ and $l^+l^-$ pairs production in ultraperipheral heavy-ion collisions at high energies. Such a channel provides a novel probe for double-parton scattering (DPS) at small $x$ enabling one to probe the photon density inside the nucleus. We have derived an analog of the standard central $pp$ pocket formula and studied the kinematical dependence of the effective cross section. Taking into account both elastic and non-elastic contributions, we have shown predictions for the DPS $cbar c l^+l^-$ production cross section differential in charm quark rapidity and dilepton invariant mass and rapidity for LHC and a future collider.