High energy resummation of transverse momentum distributions: Higgs in gluon fusion

We derive a general resummation formula for transverse-momentum distributions of hard processes at the leading logarithmic level in the high-energy limit, to all orders in the strong coupling. our result is based on a suitable generalization of high-energy factorization theorems, whereby all-order resummation is reduced to the determination of the born-level process but with incoming off-shell gluons. we validate our formula by applying it to higgs production in gluon fusion in the infinite top mass limit. we check our result up to next-to-leading order by comparison to the high energy limit of the exact expression and to next-to-next-to leading order by comparison to nnll transverse momentum (sudakov) resummation, and we predict the high-energy behaviour at next3-to-leading order. we also show that the structure of the result in the small transverse momentum limit agrees to all orders with general constraints from sudakov resummation.