Higgs production at NLL accuracy in the BFKL approach

Precision physics in the Higgs sector has been one of the main challenges of particle physics in the recent years. The pure fixed-order calculations entering the collinear factorization framework, which have been pushed up to next-cube-leading-order, are not able to describe the entire kinematic spectrum. In particular sectors, they have to be necessarily enhanced by all-order resummations. In the so-called semi-hard regime, large energy-type logarithms spoil the perturbative convergence of the series and must be resummed to all orders. This resummation is a core ingredient for a correct description of the inclusive hadroproduction of a forward Higgs boson in the limit of small Bjorken $x$, as well as for a precision study of inclusive forward emissions of a Higgs boson in association with a backward identified object. A complete resummation for these processes can be achieved at the at next-to-leading logarithmic accuracy thanks to the Balitsky-Fadin-Kuraev-Lipatov approach. In the present work we present and discuss a series of recent phenomenological results within a partial next-to-leading accuracy. They include the analysis of rapidity and azimuthal-angle differential rates for Higgs plus jet and Higgs plus charm reactions in forward and ultraforward directions of rapidity at the LHC.