Novel opportunities in the exploration of the dynamics of fundamental interactions at new-generation colliders herald the dawn of a new era for particle physics. Accessing kinematic sectors so far uncharted will open us a window of opportunities to make benchmarks of the Standard Model (SM) as well as (in)direct searches for deviations from SM predictions. Important challenges inside the SM come from the sector of strong interactions. Here, the duality between perturbative and nonperturbative aspects of Quantum Chromodynamics (QCD) leads to yet unresolved puzzles in the answer of fundamental questions, such as the origin of hadrons’ mass and spin, as well as the behavior of QCD observables in relevant kinematic corners of the phase space. In the high-energy regime, the enhancement of energy
logarithms due to diffractive semi-hard final states spoils the convergence of the perturbative series in the QCD running coupling. This calls for an improvement of the pure collinear factorization that accounts for an all-order resummation of these large logarithmic contributions. We will present recent
phenomenological analyses on rapidity, transverse-momentum and azimuthal-angle differential distributions sensitive to the inclusive emission in proton collisions of a Higgs boson or/and a heavy-flavored hadron. Our observables are calculated within the hybrid high-energy and collinear factorization, where the standard NLO collinear description is supplemented by the t-channel resummation of energy logarithms in the NLL BFKL accuracy. The fair stability that these distributions exhibit under higher-order
corrections and scale variations paves the way toward precision studies of high-energy QCD, where the hybrid factorization could serve as a common basis for the development of a multilateral formalism that combines together different resummation mechanisms.