We investigate the inclusive hadroproduction of a Higgs boson in association with a jet, featuring large transverse momenta and separated by a large rapidity distance. We propose this reaction, that can be studied at the LHC as well as at new-generation colliding machines, as a novel probe channel for the manifestation of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) dynamics. We bring evidence that high-energy resummed distributions in rapidity and transverse momentum exhibit a solid stability under higher-order corrections, thus offering us a faultless chance to gauge the feasibility of precision calculations of these observables at high energies. We come out with the message that future, exhaustive analyses of the inclusive Higgs-boson production, would benefit from the inclusion of high-energy effects in a multi-lateral formalism where distinct resummations are concurrently embodied. We propose these studies with the aim of inspiring synergies with other Communities, and pursuing the goal of widening common horizons in the exploration of the Higgs-physics sector.
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