High-energy resummation in Higgs production at NLL.

Precision physics in the Higgs sector has been one of the main challenges in the recent years. The pure fixed-order calculations entering in the $collinear factorization$ framework, which have been pushed up to N3LO, are not able to describe the entire kinematic spectrum. In particular conditions, they must be necessarily supplemented by all-order $resummations$; for instance, in the so-called $Regge$ kinematical region, large energy-type logarithms spoil the perturbative behavior of the series and must be resummed to all orders. This resummation, which can be done in the NLL through the $BFKL$ approach, is necessary to describe the inclusive hadroproduction of a forward Higgs in the limit of small Bjorken $x$, and also to study inclusive forward emissions of a Higgs boson in association with a backward identified object. We first present the full NLO result for the production of a forward Higgs boson, obtained in the infinite top-mass limit. Then, the possible extension of this calculation to the case of Higgs impact factor via gluon fusion in the central-rapidity region is also discussed.