QCD resummation effects in forward $J/psi$ and very backward jet inclusive production at the LHC

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. Our different predictions are based on the various existing mechanisms to describe the production of the $J/psi$, namely, NRQCD singlet and octet contributions, and the color evaporation model.