The inclusive Higgs boson cross-section in gluon-gluon fusion in soft-virtual approximation at fourth order in QCD

TL;DR

This work addresses the precision of the inclusive Higgs boson cross-section in gluon-gluon fusion by constructing a fourth-order soft-virtual ($N^4LO_{sv}$) approximation using four-loop gluon form factors, splitting functions, and anomalous dimensions within the Higgs effective theory. The authors analyze threshold soft-gluon emissions in Mellin space and quantify perturbative convergence and scale/PDF uncertainties, presenting predictions at $\sqrt{S}=13.6$ TeV with $m_H=125$ GeV. The main finding is that the $N^4LO_{sv}$ correction is modest (≈$-0.1\%$ relative to N3LO) but significantly reduces renormalization and factorization scale uncertainties (by about a factor of two), while the dominant residual uncertainty remains from $\alpha_s(m_Z)$ (≈$4\%$) and PDFs (a few percent depending on the set). The study highlights perturbative stability in precision Higgs phenomenology and provides cross-sections across multiple PDF sets, illustrating remaining uncertainties and the potential impact of completing the full N4LO calculation.

Abstract

We present precise results for the inclusive Higgs boson cross-section in gluon-gluon fusion at the LHC considering state-of-the-art fourth-order results in perturbative QCD arising from the dominant soft and virtual gluon emissions. Utilizing four-loop QCD results for the gluon-form factor, the splitting function and related anomalous dimensions, we study the effects of threshold enhanced soft gluon emissions and estimate their impact on the total cross-section at the fourth order. Our study highlights the role of these higher-order contributions in improving the perturbative convergence and in significantly reducing the renormalization and factorization scale uncertainties. The results provide strong evidence for the perturbative stability and reliability of Higgs boson cross-section predictions at the LHC, thereby reinforcing the robustness of theoretical inputs in precision Higgs phenomenology. We also provide cross-section predictions using a large set of available parton distribution functions and show that, together with the value of the strong coupling $α_s(m_Z)$, they cause the largest residual uncertainty for the Higgs boson cross-section in gluon-gluon fusion.