Probing the pion gluon distribution at small-$x$ in photon-induced interactions at LHC

In this paper we propose the analysis of the heavy quark photoproduction associated with a leading neutron in hadronic collisions at the LHC as an alternative to probe the pion gluon distribution in a kinematical range not covered by previous experiments. We perform an exploratory study of the charm and bottom photoproduction associated with a leading neutron in proton-proton ($pp$) and proton-lead ($pPb$) collisions, and present calculations for the rapidity distributions and cross-sections. Our predictions indicate that experimental studies of these processes are feasible, and that a future measurement of this final state will be useful to constrain the pion gluon distribution at small values of the Bjorken $x$ variable and to improve our understanding of the pion structure.