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

by Goutam Das, Sven-Olaf Moch

Submission summary

Authors (as registered SciPost users): Goutam Das
Submission information
Preprint Link: https://arxiv.org/abs/2510.17413v1  (pdf)
Date submitted: Oct. 22, 2025, 3:52 p.m.
Submitted by: Goutam Das
Submitted to: SciPost Physics Community Reports
 for consideration in Collection:
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Phenomenology
Approach: Phenomenological

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 $\alpha_s(m_Z)$, they cause the largest residual uncertainty for the Higgs boson cross-section in gluon-gluon fusion.

Current status:
Awaiting resubmission

Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-11-28 (Invited Report)

Report

The report presents an updated phenomenological analysis of the fourth-order soft-virtual correction in gluon-fusion Higgs production. The impact of the latest PDF sets since the publication of the original results, and of uncertainties in the strong coupling constant, is studied, and numerical results are provided. The text is well-written and straightforward. I recommend publication without any modification.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: top
  • significance: high
  • originality: good
  • clarity: top
  • formatting: excellent
  • grammar: excellent

Report #1 by Anonymous (Referee 1) on 2025-11-26 (Invited Report)

Strengths

A first approximation of N4LO corrections to Higgs boson productions in gluon fusion. Method worked well for lower orders. Robust computation of theoretical uncertainties stemming from scales, PDFs and alpha_s.

Weaknesses

Not much discussion about the accuracy of the approximations made. While there is evidence to support that the approximation made works at lower orders, its accuracy is difficult to quantify. In particular I did not understand from the paper whether all soft-virtual terms are actually present, or whether some residual uncertainty, even at the level of soft-virtual remains. It would be good to clarify this.

Report

The paper provides an approximation for the N4LO QCD corrections to Higgs boson gluon fusion cross section. Using this approximation it presents a computation of uncertainties stemming from PDF, alpha_s and scale variation. The estimation of these Uncertainties are robust and in line with common practices. The paper thereby presents a step forward on a previously-identified research bottleneck. It is written in a clear way. The amount of detail submitted is very minimal, but builds on ideas which were presented in previous publications. Relevant literature is cited. The conclusions are clear, remaining uncertainties suffer from PDF and alpha_s uncertainties.

Requested changes

Given that it is difficult to quantify the accuracy of the soft-virtual-type approximations made, I would recommend including a statement that a check of the corrections of the complete soft-virtual corrections, or more terms in the threshold expansion, if not the entire exact N4LO corrections, would nevertheless be desirable to have.

Recommendation

Ask for minor revision

  • validity: high
  • significance: high
  • originality: ok
  • clarity: good
  • formatting: good
  • grammar: good

Author:  Goutam Das  on 2025-11-29  [id 6086]

(in reply to Report 1 on 2025-11-26)
Category:
remark

To address the referee's recommendation, the following change is made at the very end of the Conclusion.

"Nevertheless, obtaining the complete N4LO correction would be highly desirable, as it would improve the accuracy of the soft-virtual approximation at this order."

Anonymous on 2025-12-01  [id 6090]

(in reply to Goutam Das on 2025-11-29 [id 6086])

Thank you for adding this sentence to the conclusion. Could you also add some clarification on whether there remains unknowns in the soft-virtual terms in your approximation? It seems to me that at least the delta(1-z) term may not yet be known completely from the input of splitting functions and form factor only.

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