High precision determination of the gluon fusion Higgs boson cross-section at the LHC

Abstract: We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N$^3$LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of $\pi^2$ contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N$^3$LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of $m_H = 125~{\rm GeV}$ and an LHC center-of-mass energy of $13~{\rm TeV}$, our best prediction for the gluon fusion cross-section is [ \sigma = 48.58\,{\rm pb} {}^{+2.22\, {\rm pb}\, (+4.56\%)}_{-3.27\, {\rm pb}\, (-6.72\%)} \mbox{ (theory)} \pm 1.56 \,{\rm pb}\, (3.20\%) \mbox{ (PDF+$\alpha_s$)} ]

• The paper presents a high-order QCD calculation up to N^3LO to determine the Higgs boson cross-section via gluon fusion at the LHC.
• It integrates finite quark-mass effects, electroweak corrections, and threshold resummation to minimize theoretical uncertainties.
• For a Higgs mass of 125 GeV at 13 TeV, the predicted cross-section is 48.58 pb with detailed uncertainty quantification.

High-Precision Determination of the Gluon Fusion Higgs Boson Cross-Section at the LHC

The production of the Higgs boson via gluon fusion is a critical aspect of experimental particle physics, particularly within the Large Hadron Collider (LHC) at CERN. The discussed paper presents a detailed study that aims to provide the most precise prediction available for the Higgs boson cross-section in gluon-fusion production mode at the LHC, achieved through state-of-the-art perturbative expansions. Here, the authors have pushed the boundaries of precision through extremely high-order calculations in Quantum Chromodynamics (QCD).

Perturbative Expansion and Uncertainties

The authors employ a perturbative expansion up to N$^3$LO (next-to-next-to-next-to-leading order) in QCD, using an effective theory where the top-quark is considered infinitely heavy, simplifying the calculations. This is combined with next-to-leading order (NLO) QCD corrections for actual finite quark-mass effects. Additional electroweak corrections and leading inverse top-quark mass corrections are incorporated at three loops. Importantly, the study carefully assesses the uncertainty arising from uncomputed higher-order corrections both from perturbative QCD beyond N$^3$LO and from unknown mixed QCD-electroweak effects. They also study the sensitivity of their predictions to different parton distribution function (PDF) sets and assess the parametric uncertainties arising from the determination of the strong coupling constant and quark masses.

Threshold Resummation

The research includes an investigation into the effects of threshold resummation, considering both traditional QCD frameworks and the soft-collinear effective theory (SCET) approach, which resums specific classes of $\pi^2$ contributions to all orders. These methodologies further aid in reducing theoretical uncertainties.

Numerical Results

For a Higgs mass of 125 GeV at a center-of-mass energy of 13 TeV, their best prediction for the gluon fusion cross-section is

$\sigma = 48.58\,\text{pb} \,{}^{+2.22\,\text{pb}\,(+4.56\%)}_{-3.27\,\text{pb}\,(-6.72\%)} \text{ (theory)} \pm 1.56 \,\text{pb}\, (3.20\%) \text{ (PDF+%%%%3%%%%)}$

This result represents the culmination of several advanced calculations, improvements in estimating various systematic uncertainties, and the application of high-precision theoretical methods.

Implications and Future Prospects

The paper's findings contribute significantly to the understanding of Higgs boson production at such high theoretical precision, potentially giving a robust foundation for future experimental verifications and analyses. They offer crucial insights for improving the Standard Model's predictions concerning the LHC's outputs and indirectly contributing to detecting new physics beyond the Standard Model by providing high-precision baselines.

Looking forward, further advancements could arise from analogous computations with closed analytical forms for the cross-section and full NNLO QCD cross-section computation in a fully massive theory. Additionally, the exact inclusion of bottom and charm quark effects beyond the EFT approximation would further refine these predictions. These expansions, alongside more precise future LHC data, will iteratively improve theoretical predictions and possibly point towards new phenomena in particle physics.