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Abstract 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.