  The agreement between calculations inspired by the resummation of energy
logarithms, known as BFKL approach, and experimental data in the semi-hard
sector of QCD has become manifest after a wealthy series of phenomenological
analyses. However, the contingency that the same data could be concurrently
portrayed at the hand of fixed-order, DGLAP-based calculations, has been
pointed out recently, but not yet punctually addressed. Taking advantage of the
richness of configurations gained by combining the acceptances of CMS and
CASTOR detectors, we give results in the full next-to-leading logarithmic
approximation of cross sections, azimuthal correlations and azimuthal
distributions for three distinct semi-hard processes, each of them featuring a
peculiar final-state exclusiveness. Then, making use of disjoint intervals for
the transverse momenta of the emitted objects, i.e. $\kappa$-windows, we
clearly highlight how high-energy resummed and fixed-order driven predictions
for semi-hard sensitive observables can be decisively discriminated in the
kinematic ranges typical of current and forthcoming analyses at the LHC. The
scale-optimization issue is also introduced and explored, while the uncertainty
coming from the use of different PDF and FF set is deservedly handled. Finally,
a brief overview of JETHAD, a numerical tool recently developed, suited for the
computation of inclusive semi-hard reactions is provided.
