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The study of the dynamics of strong interactions in the high-energy regime isa core line of frontier researches at the LHC as well as at new-generationcolliding facilities. Here, the enhancement of energy logarithms due todiffractive semi-hard final states spoils the convergence of the perturbativeseries in the QCD running coupling, thus calling for an improvement of the purecollinear factorization that accounts for an all-order resummation of theselarge logarithmic contributions. Motivated by the recent discovery thatinclusive emissions of heavy-flavored particles allow for clear signals of astabilization of high-energy resummed differential distributions underhigher-order corrections and scale variations, we provide novel predictions ofrapidity and azimuthal-angle observables for the inclusive hadroproduction of alight meson ($\eta$ or $\pi^\pm$) in association with a heavy-flavored hadron($\Lambda_c$ or $b$-flavored hadron). We calculate our observables in a hybridhigh-energy and collinear factorization framework, where next-to-leadingBFKL-resummed partonic cross sections are convoluted with collinear partondistributions and fragmentation functions. We consider kinematic rangestypically covered by acceptances of LHC detectors, and new ones coming from thecombined tag of an ultra-forward particle at the future Forward PhysicsFacility (FPF) and of a central one at ATLAS via a tight timing-coincidencesetup. By performing a detailed study on uncertainties associated to collinearinputs via a replica-driven analysis, as well as on ones intrinsically comingfrom the high-energy resummation, we highlight the challenges and the stepsrequired to gauge the feasibility of precision studies of our processes.

High-energy emissions of light mesons plus heavy flavor at the LHC and the Forward Physics Facility