An approximate NNNLO cross section for Higgs production in gluon fusion

TL;DR

This paper presents an approximate NNNLO calculation for Higgs production in gluon fusion, combining known resummation behaviors to improve accuracy and reduce uncertainties, indicating higher corrections than previously estimated.

Contribution

The authors develop an approximate NNNLO cross section for Higgs production that incorporates both soft-gluon and high-energy resummations, enhancing precision over existing NNLO results.

Findings

Cross section increases by 6-13% at 8 TeV LHC for Higgs mass 125 GeV.

Significant reduction in theoretical scale uncertainty.

Higher order corrections may be larger than current estimates.

Abstract

An approximate expression for the inclusive Higgs production cross section in gluon fusion at NNNLO in QCD with finite top mass is presented. We argue that an accurate approximation can be constructed combining (and improving) the large- and small-z behaviours of the partonic cross section, which are both known to all orders from soft-gluon (Sudakov) and high-energy (BFKL) resummations, respectively. For a 125 GeV Higgs at LHC at 8 TeV, we find an increase of about 6-13% with respect to the NNLO inclusive cross section for the conventional scale \mu_R=m_H/2, suggesting that higher order QCD corrections might be underestimated by presently available results. We also find a significant reduction of the scale uncertainty.