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Higgs production via vector-boson fusion at the LHC

by Gaetano Barone, Jiayi Chen, Stephane Cooperstein, Nikita Dolganov, Silvia Ferrario Ravasio, Yacine Haddad, Stefan Höche, Barbara Jäger, Alexander Karlberg, Alexander Mück, Mathieu Pellen, Christian T. Preuss, Daniel Reichelt, Simon Reinhardt, Marco Zaro

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Submission summary

Authors (as registered SciPost users): Gaetano Barone · Alexander Karlberg · Mathieu Pellen · Daniel Reichelt · Marco Zaro
Submission information
Preprint Link: https://arxiv.org/abs/2507.22574v1  (pdf)
Data repository: https://gitlab.cern.ch/LHCHIGGSXS/LHCHXSWG1/VBFStudyYR5
Date submitted: Aug. 11, 2025, 10:55 a.m.
Submitted by: Mathieu Pellen
Submitted to: SciPost Physics Community Reports
 for consideration in Collection:
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Experiment
  • High-Energy Physics - Phenomenology
Approach: Phenomenological

Abstract

In this article, we summarise the recent experimental measurements and theoretical work on Higgs boson production via vector-boson fusion at the LHC. Along with this, we provide state-of-the-art predictions at fixed order as well as with parton-shower corrections within the Standard Model at 13.6 TeV. The results are presented in the form of multi-differential distributions as well as in the Simplified Template Cross Section bins. All materials and outputs of this study are available on public repositories. Finally, following findings in the literature, recommendations are made to estimate theoretical uncertainties related to parton-shower corrections.

Current status:
Has been resubmitted

Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-9-22 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2507.22574v1, delivered 2025-09-22, doi: 10.21468/SciPost.Report.11987

Strengths

  • Comprehensive discussion of impact of both fixed-order corrections and different parton showers and matching procedures.
  • Comprehensive analysis of full EW production versus VBF production.
  • Recommendations for assigning uncertainties from samples generated using NLO+PS Monte Carlo tools.
  • Valuable contribution to further Higgs studies through vector boson fusion.

Weaknesses

  • No major weaknesses, see below for comments on minor comments.

Report

The authors present a comprehensive set of studies concerning precision predictions of Higgs boson production in vector boson fusion (VBF). They distinguish between VBF production and the "full" electroweak (EW) production of Hjj final states. The former are predicted with NNLO QCD and NLO EW accuracy at fixed order as well as NLO QCD and EW accuracy merged with parton showers (NLO+PS). The authors discuss the impact of various higher-order corrections and compare full EW production with VBF production at various perturbative orders, as well as analyzing the impact of parton showers, doing so at the level of STXS as well as with typical fiducial cuts. The authors pay particular attention to, and provide recommendations for, the estimation of uncertainties in parton showers.

This work provides an invaluable contribution to the Higgs Report through the VBF subgroup, and will no doubt be an important reference for future analyses. It is clear and well-written, and I can recommend publication in SciPost. Prior to publication, however, I ask that the authors address a few minor comments (see below).

Requested changes

  • On p.4, towards the end of sec 2.1, the authors write "We note that both types of calculations are close...". To avoid any misunderstanding, could the authors clarify that it is the results of these calculations (as opposed to e.g. the methods used for the calculations) that are close.
  • The second sentence of sec 2.2 may be misunderstood to imply that Table 1 summarizes the sensitivity across all production modes, especially given the following sentence "This unprecedented precision achieved with the proton-proton collision data recorded at the LHC Run 1 and Run 2 allowed for a more precise investigation of these production mechanisms." From the caption of this table, it is clear that the table refers only the VBF production, but I ask that the authors make this clear in the text too.
  • At the top of p. 6, the authors state that in their Ref. [15], the parton-shower modeling uncertainty was estimated to be 12%, which is larger than the results of their study. Is this connected with the use of the global recoil in PYTHIA, which (as the authors mention several times) should be avoided for VBF-like processes? If so, I ask that the authors mention this, either in section 6 or in their conclusions.
  • At the top of p.7, the authors discuss fixed-order computations including the Higgs decay. They erroneously state that Ref. [52] includes NNLO corrections to both production and decay processes. In fact, this reference treats the production at NNLO and the decay at LO. The NNLO corrections were included in Ref [87] of the present study.
  • On p. 8, the authors write "In Ref. [69], the gluon-gluon induced contribution for Higgs production was computed for the first time." Somewhat pedantically, I ask that the authors clarify that they mean Higgs production through VBF.
  • On p.9, the authors write "Another direction of improvements involves the inclusion of s- and t-channel contributions [60, 83] alongside the ones defining the VBF topology." This is somewhat confusing as the authors previously stated (in sec. 2.1) that the VBF topology is defined by the t- and u-channel contributions. Could the authors please clarify this.
  • On p. 11, the authors refer to a "simple shower". Could the authors either briefly explain what they mean by this, or provide a reference that the reader could consult.
  • Could the authors state that the contribution with superscript "NF VBF" in Eq 11 refers to the non-factorizable part of the VBF contribution at NNLO?
  • On p. 20, the authors write "On the other hand, the loop-induced contributions squared, ... are of the order of the EW contribution, ..." I assume that they mean the NLO EW correction?
  • A possible typo: at the bottom of p.22, the authors write "The second-to-lowest panel illustrates that the VH contribution...". Did they mean third-to-lowest (i.e. the one labeled "Full/VBF")?

Recommendation

Publish (surpasses expectations and criteria for this Journal; among top 10%)

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

Author:  Mathieu Pellen  on 2025-10-06  [id 5892]

(in reply to Report 2 on 2025-09-22)
Category:
answer to question

Dear editor,

we would like to first thank both referees for their feedbacks and suggestions. Below we have addressed all of them together and marked them in red in the new version of the manuscript.

  • On p.4, towards the end of sec 2.1, the authors write "We note that both types of calculations are close...". To avoid any misunderstanding, could the authors clarify that it is the results of these calculations (as opposed to e.g. the methods used for the calculations) that are close.

This has been fixed.

  • The second sentence of sec 2.2 may be misunderstood to imply that Table 1 summarizes the sensitivity across all production modes, especially given the following sentence "This unprecedented precision achieved with the proton-proton collision data recorded at the LHC Run 1 and Run 2 allowed for a more precise investigation of these production mechanisms." From the caption of this table, it is clear that the table refers only the VBF production, but I ask that the authors make this clear in the text too.

This has been fixed.

  • At the top of p. 6, the authors state that in their Ref. [15], the parton-shower modeling uncertainty was estimated to be 12%, which is larger than the results of their study. Is this connected with the use of the global recoil in PYTHIA, which (as the authors mention several times) should be avoided for VBF-like processes? If so, I ask that the authors mention this, either in section 6 or in their conclusions.

The 12% uncertainty does not stem from the use of the global recoil. Although hadronisation effects might have been tuned with the global recoil effect in the past, the effect here is most probably driven by the separate evaluation of the matching uncertainties, which are evaluated by comparing MG5_aMC@NLO+HERWIG7 against POWHEG-BOX+Pythia8 [15]. This scheme does not take into account compounded effects. In the tight phase-space of this measurement along with the remainder of uncertainties considered in [15], that results in this 12% effect. A paragraph hinting at this was already present in the manuscript right before the conclusion. A footnote making this clear has been added.

  • At the top of p.7, the authors discuss fixed-order computations including the Higgs decay. They erroneously state that Ref. [52] includes NNLO corrections to both production and decay processes. In fact, this reference treats the production at NNLO and the decay at LO. The NNLO corrections were included in Ref [87] of the present study.

This has been fixed.

  • On p. 8, the authors write "In Ref. [69], the gluon-gluon induced contribution for Higgs production was computed for the first time." Somewhat pedantically, I ask that the authors clarify that they mean Higgs production through VBF.

We thank the referee for finding this out. This was a mistake, this has now been corrected and extended for clarity.

  • On p.9, the authors write "Another direction of improvements involves the inclusion of s- and t-channel contributions [60, 83] alongside the ones defining the VBF topology." This is somewhat confusing as the authors previously stated (in sec. 2.1) that the VBF topology is defined by the t- and u-channel contributions. Could the authors please clarify this.

This has been fixed.

  • On p. 11, the authors refer to a "simple shower". Could the authors either briefly explain what they mean by this, or provide a reference that the reader could consult.

We modified the paragraph. It is now clear that the simple shower is the default Pythia shower, based on DGLAP kernels, of Ref [132] (hep-ph/0408302).

  • Could the authors state that the contribution with superscript "NF VBF" in Eq 11 refers to the non-factorizable part of the VBF contribution at NNLO?

This has been fixed.

  • On p. 20, the authors write "On the other hand, the loop-induced contributions squared, ... are of the order of the EW contribution, ..." I assume that they mean the NLO EW correction?

This has been fixed.

  • A possible typo: at the bottom of p.22, the authors write "The second-to-lowest panel illustrates that the VH contribution...". Did they mean third-to-lowest (i.e. the one labeled "Full/VBF")?

This has been fixed.

In addition to the changes described above, Ref. [202] has been updated.

Best regards, the authors

Attachment:

vbf-higgs-wg.pdf

Anonymous on 2025-10-07  [id 5895]

(in reply to Mathieu Pellen on 2025-10-06 [id 5892])

Dear authors,

I believe that the following comment has not been addressed in the manuscript:

  • At the top of p.7, the authors discuss fixed-order computations including the Higgs decay. They erroneously state that Ref. [52] includes NNLO corrections to both production and decay processes. In fact, this reference treats the production at NNLO and the decay at LO. The NNLO corrections were included in Ref [87] of the present study.

Best wishes, Reviewer #2

Author:  Mathieu Pellen  on 2025-10-08  [id 5900]

(in reply to Anonymous Comment on 2025-10-07 [id 5895])

Dear referee,

I believe the new version is correct. While we did not marked it in red (apologies for this), in the latest version, reference [52] is now: [52] K. Asteriadis, A. Behring, K. Melnikov, I. Novikov and R. Röntsch, QCD corrections to Higgs boson production and H→bb¯ decay in weak boson fusion, Phys. Rev. D 110(5), 054017 (2024), doi:10.1103/PhysRevD.110.054017, 2407.09363. i.e. the reference [87] of v1: [87] K. Asteriadis, A. Behring, K. Melnikov, I. Novikov and R. Röntsch, QCD corrections to Higgs boson production and H→bb¯ decay in weak boson fusion, Phys. Rev. D 110(5), 054017 (2024), doi:10.1103/PhysRevD.110.054017, 2407.09363. which should be correct according to your remark. If we are missing something, please let us know.

Best regards, Mathieu Pellen

Report #1 by Anonymous (Referee 1) on 2025-9-4 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2507.22574v1, delivered 2025-09-04, doi: 10.21468/SciPost.Report.11870
Disclosure of Generative AI use

The referee discloses that the following generative AI tools have been used in the preparation of this report:

ChatGPT 5 for spell checking.

Report

The paper “Higgs production via vector-boson fusion at the LHC" by Barone et al. presents a comprehensive review and state-of-the-art predictions for Higgs boson production via vector-boson fusion (VBF) at the Large Hadron Collider (LHC). VBF is one of the most critical Higgs production channels, enabling a direct study of the gauge-Higgs sector through its distinctive phenomenology. The authors survey recent ATLAS and CMS measurements and discuss the theoretical developments towards improved theoretical precision. Fixed-order Standard Model predictions at 13.6 TeV, including QCD and electroweak corrections, are systematically surveyed, including interference effects and the validity of the typically employed VBF approximation. In addition, predictions matched to parton showers are examined using event generators, also assessing relevant uncertainties.

A comprehensive range of results is presented, including reference to Simplified Template Cross Sections. I personally find those not tremendously useful, but if experimentalists need them, they can find them in this work. The paper also issues broader recommendations through the LHCHWG process.

This paper documents a comprehensive analysis of an important Higgs physics channel with direct relevance for the corresponding experimental efforts. The results reported here are not new, but the authors have compiled them into a valuable reference document that will be appreciated by many. I recommend publication in SciPost as a Community Report.

Requested changes

Small typos:

  • "University University" in affiliation 1
  • "angular-orderd" -> "angular-ordered"
  • "sof-physics" -> "soft-physics"
  • "upper part part" -> "upper part"
  • "measurments" -> "measurements"
  • "two calculations are available for the the differential" > "two calculations are available for the differential" (duplicated `the')

There is also a mix of British and American English spelling. The authors may prefer to settle for one, but that's not particularly relevant.

Recommendation

Publish (meets expectations and criteria for this Journal)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Author:  Mathieu Pellen  on 2025-10-06  [id 5893]

(in reply to Report 1 on 2025-09-04)

Dear editor,

we would like to first thank both referees for their feedbacks and suggestions. Below we have addressed all of them together and marked them in red in the new version of the manuscript.

  1. "University University" in affiliation 1
  2. "angular-orderd" -> "angular-ordered"
  3. "sof-physics" -> "soft-physics"
  4. "upper part part" -> "upper part"
  5. "measurments" -> "measurements"
  6. "two calculations are available for the the differential" > "two calculations are available for the differential" (duplicated `the')

All typos have been corrected.

In addition to the changes described above, Ref. [202] has been updated.

Best regards, the authors

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