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arxiv: 2604.24421 · v1 · submitted 2026-04-27 · ✦ hep-ph

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Double SM-like Higgs Production at future e^+ e^- colliders in the 3-Higgs Doublet Model under the S₃ symmetry

Emine Yildirim
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:51 UTC · model grok-4.3

classification ✦ hep-ph
keywords double Higgs production3-Higgs doublet modelS3 symmetryfuture e+e- collidersbeyond Standard ModelSM-like Higgscross section deviations
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The pith

In the S3-symmetric three-Higgs-doublet model, double SM-like Higgs production cross sections at future e+e- colliders can differ from the Standard Model by orders of magnitude.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines double production of the SM-like Higgs boson in the S3-3H model at proposed electron-positron colliders. It first identifies the allowed parameter space by imposing perturbative unitarity, vacuum stability, and existing collider constraints from LHC and Tevatron. Within this space, the cross sections for the processes e+e- to hhZ and e+e- to hh nu nu can be enhanced or suppressed by several orders of magnitude compared to the Standard Model. This matters because such large deviations would make these rare processes much more accessible experimentally, providing a direct test of extended Higgs sectors at future facilities.

Core claim

The authors find that, in the S3-symmetric three-Higgs-doublet model without CP violation, after scanning the numerically allowed parameter space consistent with theoretical and experimental bounds, the double SM-like Higgs production rates in the hhZ and hhνν channels at future e+e- colliders can deviate from SM predictions by up to a few orders of magnitude, indicating that measurable signals of this beyond-Standard-Model scenario are possible.

What carries the argument

The S3-symmetric three-Higgs-doublet model, which reduces the number of free parameters in the Higgs potential via the discrete S3 symmetry and allows for a SM-like lightest Higgs while generating large contributions to double Higgs production from the additional scalars.

If this is right

  • The e+e- → hhZ channel can show significantly enhanced cross sections, potentially observable with lower integrated luminosity.
  • The e+e- → hhν_e ν̄_e channel similarly allows for large deviations from SM expectations.
  • These deviations persist across the viable parameter space, making the processes sensitive probes of the model.
  • Precision studies at future colliders could either discover or further constrain the S3-3H scenario.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Observing such deviations would suggest the presence of additional Higgs doublets arranged under S3 symmetry rather than other BSM frameworks.
  • Non-observation would tighten bounds on the trilinear Higgs couplings in multi-doublet models.
  • The analysis could be extended to include CP-violating phases or other collider energies to broaden the testable range.
  • Connections to other observables like triple Higgs production might reveal correlated signatures.

Load-bearing premise

The lightest CP-even Higgs is assumed to be exactly SM-like, and the chosen scan points are taken to represent the full range of allowed deviations after constraints.

What would settle it

Precise measurement of the cross section for e+e- → hhZ at 500 GeV that agrees with the Standard Model within 10-20% accuracy would exclude the regions of the S3-3H parameter space that predict large enhancements.

Figures

Figures reproduced from arXiv: 2604.24421 by Emine Yildirim.

Figure 1
Figure 1. Figure 1: FIG. 1. Blue: Allowed regions from unitarity and stability in the S3-3H moedel. As for the view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Green: Allowed regions from collider experiments. The red, blue and black con view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Feynman diagrams for view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The upper panels show cross section for the view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The left and middle panels show the cross section for the process view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Feynman diagrams for view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The left panel shows cross section for the view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Cross sections for the process view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. We indicate the contour plot of view at source ↗
read the original abstract

In this paper, we present the production of double SM-like Higgs $ (h) $ at the future electron positron colliders within the context of $ S_{3} $ model with three Higgs doublets (S3-3H) and no CP violation to describe beyond the Standard Model Higgs Physics. We focus first on the numerically allowed parameter space of the model, taking into account theoretical bounds from perturbative unitarity and vacuum stability, as well as by data at the Large Hadron Collider (LHC) and the Tevatron. The double Higgs production in the S3-3H model can deviate from the SM predictions up to a few orders of magnitude in both the $ e^+e^- \rightarrow hhZ $ and the $ e^+ e^- \rightarrow h h\nu_{e} \bar{\nu}_{e}$ channels. Thus, our findings indicate that the S3-3H model can lead to measurable deviations from the SM predictions of Higgs production at future $ e^+ e^- $ colliders. These results highlight the importance of studies at such colliders for searching physics beyond the Standard Model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper investigates double production of the SM-like Higgs boson in the S3-symmetric three-Higgs-doublet model (S3-3H) at future electron-positron colliders. After scanning the parameter space subject to perturbative unitarity, vacuum stability, and LHC/Tevatron constraints with the lightest CP-even Higgs being SM-like, the authors find that the cross sections for e+e− → hhZ and e+e− → hhνeν̄e can deviate from Standard Model predictions by up to several orders of magnitude.

Significance. If the reported large deviations are representative of the allowed parameter space, this work would demonstrate that the S3-3H model offers testable predictions for enhanced double Higgs production at future colliders such as the ILC, providing a potential avenue to distinguish this BSM scenario from the SM.

major comments (1)
  1. [Numerical scan and results (Section 4)] The manuscript identifies specific points in the allowed parameter space where the cross-section ratios reach O(10–1000), but does not report the fraction of scanned points exhibiting such enhancements, nor any distribution or density measure of the cross-section ratios across the viable region. This omission leaves open whether the large deviations are generic or confined to isolated, finely tuned points, directly impacting the strength of the claim that the model 'can lead to measurable deviations'.
minor comments (2)
  1. [Abstract] The abstract states that deviations occur 'up to a few orders of magnitude' but gives no quantitative details on the scan implementation, number of points sampled, or how LHC/Tevatron bounds are imposed after the theoretical constraints; a brief clarification would strengthen the presentation.
  2. [Model description (Section 2)] Notation for the additional Higgs doublets (e.g., their vevs and mixing angles) is introduced but could be summarized in a single table early in the model section for easier reference when reading the production cross-section formulas.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive overall assessment of our manuscript. We address the major comment below and will incorporate the suggested improvements in the revised version.

read point-by-point responses

  1. Referee: [Numerical scan and results (Section 4)] The manuscript identifies specific points in the allowed parameter space where the cross-section ratios reach O(10–1000), but does not report the fraction of scanned points exhibiting such enhancements, nor any distribution or density measure of the cross-section ratios across the viable region. This omission leaves open whether the large deviations are generic or confined to isolated, finely tuned points, directly impacting the strength of the claim that the model 'can lead to measurable deviations'.

    Authors: We agree that including quantitative information on the distribution of the cross-section ratios would strengthen the presentation and better contextualize the benchmark points. Our numerical scan was designed to delineate the viable parameter space after imposing all theoretical and experimental constraints, with the selected points chosen to demonstrate the maximum possible deviations within that space. To address the referee's concern, in the revised manuscript we will add a new figure (or subsection) in Section 4 displaying the histogram of the ratio σ_{S3-3H}/σ_{SM} for both the hhZ and hhνν channels over the full set of viable points, together with the fraction of points exhibiting enhancements above thresholds such as 10, 100, and 1000. This will clarify the prevalence of large deviations without altering the core claim that the model can produce measurable effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard external-constraint scan followed by forward prediction

full rationale

The paper first restricts the S3-3H parameter space using perturbative unitarity, vacuum stability, and external LHC/Tevatron data that force the lightest CP-even Higgs couplings to be SM-like. It then computes the e+e− → hhZ and hhνν cross sections from the surviving points. This workflow does not reduce any prediction to its inputs by construction: the double-Higgs rates depend on trilinear couplings that remain free after the single-Higgs constraints are applied. No self-definitional equations, no fitted quantities renamed as predictions, and no load-bearing self-citations appear in the derivation. The representativeness of the chosen scan points is a separate statistical-coverage question, not a circularity issue.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 1 invented entities

The model rests on an S3-symmetric scalar potential with multiple free parameters that are scanned numerically; the lightest Higgs is required to be SM-like by construction.

free parameters (1)
  • Higgs potential couplings and vacuum expectation values
    Several independent parameters in the 3HDM potential remain after S3 symmetry is imposed and are constrained only by bounds rather than fixed.
axioms (3)
  • domain assumption S3 symmetry governs the Higgs sector
    Imposed to reduce the number of free parameters in the potential.
  • domain assumption No CP violation
    Explicitly stated as part of the model definition.
  • domain assumption Lightest CP-even Higgs is SM-like
    Required for consistency with LHC observations.
invented entities (1)
  • Two additional Higgs doublets no independent evidence
    purpose: Extend the SM Higgs sector under S3 symmetry
    Postulated to realize the 3HDM; no independent experimental evidence provided.

pith-pipeline@v0.9.0 · 5511 in / 1523 out tokens · 46573 ms · 2026-05-08T02:51:10.146403+00:00 · methodology

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Reference graph

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