  In this paper we study a general framework to perform leading log high energy
resummation with complete dependence from the rapidity and the transverse
momentum of the studied system. As an application, high energy resummed
expression for the Higgs boson production in the effective field theory
framework will be derived. Explicit result for this process will be
cross-checked against fixed order evaluations up to NNLO. Consistency with
known high energy resummation for single differential rapidity or transverse
momentum distribution, as well as for inclusive cross section, will also be
shown.
