Higgs production in gluon fusion beyond NNLO

TL;DR

This paper develops an approximate N$^3$LO calculation for Higgs production via gluon fusion, incorporating finite top mass effects, and demonstrates its impact on cross section predictions and scale dependence.

Contribution

It introduces a novel approximation method for N$^3$LO Higgs production cross section using Mellin space analyticity and resummation insights, extending beyond previous NNLO calculations.

Findings

N$^3$LO correction increases the cross section by about 16%.

The approximation reduces the theoretical scale uncertainty.

The method aligns well with known NNLO results.

Abstract

We construct an approximate expression for the cross section for Higgs production in gluon fusion at next-to-next-to-next-to-leading order (N$^3$LO) in $\alpha_s$ with finite top mass. We argue that an accurate approximation can be constructed by exploiting the analiticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations. We support our argument with an explicit comparison of the approximate and the exact expressions up to the highest (NNLO) order at which the latter are available. We find that the approximate N$^3$LO result amounts to a correction of 16% to the NNLO QCD cross section for production of a 125 GeV Higgs at the LHC (8 TeV), larger than previously estimated, and it significantly reduces the scale dependence of the NNLO result.