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

Abstract

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 by comparison to NNLL order trasverse momentum (Sudakov) resummation, and we predict the high-energy behaviour at next${}^3$-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.

28 pages, 6 figures, Final version published in JHEP: several typos corrected (including in equations)

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• Higgs boson production in association with a jet at next-to-next-to-leading order
• Higgs production via gluon-gluon fusion with finite top mass beyond next-to-leading order
• Small x Resummation with Quarks: Deep-Inelastic Scattering
• High Energy Resummation of Drell-Yan Processes
• Small x resummation of rapidity distributions: the case of Higgs production
• Resummation ambiguities in the Higgs transverse-momentum spectrum in the Standard Model and beyond

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