Approximating missing higher-orders in transverse momentum distributions using resummations

TL;DR

This paper introduces a new method combining multiple resummation techniques to approximate the unknown N3LO transverse momentum distribution for Higgs and Drell-Yan processes, improving accuracy and reducing scale dependence.

Contribution

It develops a novel approximation method that integrates threshold, small-pt, and high energy resummations based on Mellin space singularity analysis.

Findings

Approximate N3LO distribution differs by a few percent from NNLO for Higgs production.

The method reduces theoretical uncertainties related to scale dependence.

Provides a more reliable prediction for transverse momentum distributions.

Abstract

We present a more reliable approach to approximate the unknown next-to-next-to-next-to-leading order (N3LO) transverse momentum distribution of colourless final states, namely the Higgs boson produced via gluon fusion and the lepton pair produced via Drell--Yan (DY) mechanism. The approximation we construct relies on the combination of various resummation formalisms -- namely threshold, small-pt and high energy resummations -- by exploiting the singularity structure of the large logarithms in Mellin space. We show that for the case of Higgs boson production, the approximate N3LO transverse momentum distribution amounts to a correction of a few percent with respect to the NNLO result with a reduction in the scale dependence.