  We study the inclusive production, at hadron colliders, of a Higgs boson and
a jet widely separated in rapidity. Kinematic sectors explored fall into the
so-called semi-hard regime, where both fixed-order and high-energy dynamics
come into play. Therefore, we propose a first version of a matching procedure
aimed at combining NLO fixed-order computations, as obtained from POWHEG, with
the NLL resummation of energy logarithms via JETHAD. According to our
knowledge, this represents a novel implementation of a matching in the context
of the high-energy resummation at NLL and for rapidity-separated two-particle
final states.
