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

TL;DR

This paper develops a high-energy resummation formula for transverse momentum distributions in hard processes, validated on Higgs production via gluon fusion, extending accuracy to next-to-next-to-leading order and beyond.

Contribution

It introduces a general resummation approach for transverse momentum distributions at high energy, applicable to Higgs production, with validation up to NNLL order and predictions at N$^3$LO.

Findings

Validated the resummation formula against known NLO and NNLO results.

Predicted high-energy behavior at N$^3$LO.

Confirmed small transverse momentum structure matches Sudakov resummation constraints.

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.