The inclusive production at the LHC of a charged light hadron and of a jet, featuring a wide separation in rapidity, is suggested as a new probe process for the investigation of the BFKL mechanism of resummation of energy logarithms in the QCD perturbative series. We present some predictions, tailored on the CMS and CASTOR acceptances, for the cross section averaged over the azimuthal angle between the identified jet and hadron and for azimuthal correlations. • both the hadron and the jet tagged by the CMS detector in their typical kinematic configurations, i.e.: k min H = 5 GeV, k min J = 35 GeV, y max H = −y min H = 2.4, y max J = −y min J = 4.7 [42]. For the sake of brevity, we will refer to this choice as the CMS-jet configuration;• a hadron always detected inside CMS in the range given above, together with a very R , √ s = 13 TeV, and Y ≤ 7.1 (CMS-jet configuration). backward jet tagged by CASTOR. In this peculiar, CASTOR-jet configuration, the jet lies in the typical range of the CASTOR experimental analyses, i.e. k min J = 5 GeV, y max J = −5.2, y min J = −6.6 [44],The value of k max H is constrained by the lower cutoff of the adopted FF parametrizations (see below) and is always fixed at 21.5 GeV. The value of k max J is instead constrained by