Forward $J/psi$ and very backward jet inclusive production at the LHC

In the spirit of Mueller-Navelet dijet production, we propose and study the inclusive production of a forward $J/psi$ and a very backward jet at the LHC as an observable to reveal high-energy resummation effects `a la BFKL. We obtain several predictions, which are based on the various mechanisms discussed in the literature to describe the production of the $J/psi$, namely, NRQCD singlet and octet contributions, and the color evaporation model.