Higgs boson production at next-to-leading logarithmic accuracy

It has been recently argued that the inclusive hadroproduction at the LHC of a Higgs boson in association with a jet can be sensitive to the high-energy dynamics. Moreover, the impact of the resummation at FCC energies is expected to be large also in the inclusive cross section for the main Higgs production channel in proton-proton collisions, namely the gluon fusion. As the energy increases, a pure $k_t$-factorization framework or a collinear-factorization approach supplemented by the high-energy resummation are adequate formalisms to describe these processes. In both cases, the fundamental missing ingredient for a next-to-leading logarithmic description is the Higgs boson impact factor. We present the full next-to-leading result for the forward Higgs impact factor, obtained in the infinite top-mass limit, discussing possible future extensions, such as the calculation of the impact factor in the central rapidity region.