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

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 \alpha_{\rm s}(m_Z) , they cause the largest residual uncertainty for the Higgs boson cross-section in gluon-gluon fusion.