Estimating the BFKL effects on the vector meson + jet production in photon - induced interactions at the LHC

The associated vector meson + jet production in photon - induced interactions at the LHC is investigated and predictions for the cross - sections are derived considering the NLO corrections to the BFKL kernel. We explore the possibility that in a near future the FOCAL detector could be used to measure the jet at forward rapidities, with the associated meson being measured by a central or forward detector, and estimate the rapidity distributions for the $\rho$ + jet and $J\mathrm{/}\mathrm{\Psi }$ + jet photoproduction in $pp$, $Pbp$ and $PbPb$ collisions. We demonstrate that the associated cross-sections are non - negligible and that a future experimental analysis can be useful to constrain the description of the BFKL kernel and improve our understanding of the QCD dynamics.