Investigating extended scalar sectors at current and future colliders

Tania Robens

REVIEW 3 major objections 4 minor 1 cited by

Investigating extended scalar sectors at current and future colliders

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A simple two-real-scalar extension of the Standard Model could produce scalar-to-scalar decays at rates up to about 60 pb at the 13 TeV LHC while evading all current constraints, a gap that dedicated searches should close.

desk verdict Useful proceedings summary of singlet and inert doublet constraints; the standout 60 pb scalar-to-scalar rates are imported from the companion paper and deserve a cross-check. read the letter →

arxiv 1908.10809 v1 pith:IZR72DBZ submitted 2019-08-28 hep-ph

Tania Robens This is my paper · ORCID

classification hep-ph

keywords extendedscalarsectorsHiggsbosonLHCsearchesInertDoubletModelsingletextensionscalar-to-scalardecaysfuturee+e-collidersdarkmattercandidate

open problems Dark Matter

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This short report maps what current and future collider limits say about three simple extensions of the Standard Model's scalar sector: adding one real singlet scalar, adding an inert second doublet, and adding two real singlet scalars. The paper compiles the parameter-space regions that survive theoretical constraints and existing experimental searches, and it points to where those searches miss viable possibilities. The central point is that the two-real-scalar model can produce scalar-to-scalar decays such as $p p \to h_3 \to h_1 h_2$ and $p p \to h_a \to h_b h_b$ at rates of order tens of picobarns at the 13 TeV LHC, with no current search targeting exactly these final states. The author encourages dedicated experimental searches using the existing Run 2 dataset and argues that future $e^+e^-$ colliders could probe the inert doublet model down to production cross sections near one femtobarn.

What carries the argument

The load-bearing object is the scalar potential of the two-real-scalar model with a $Z_2\otimes Z_2'$ symmetry. After the doublet and the two singlet fields take vacuum expectation values and mix, the three neutral mass eigenstates $h_1,h_2,h_3$ couple to Standard Model particles through rescaling factors $\kappa_i$, with orthogonality enforcing $\sum_i \kappa_i^2 = 1$; the measured 125 GeV scalar must have $|\kappa_{125}| \gtrsim 0.96$. The new signatures come from the trilinear scalar couplings among these eigenstates, which allow a heavier state to decay into two lighter ones, $h_3 \to h_1 h_2$ or $h_a \to h_b h_b$, with the light scalars subsequently decaying into Standard Model particles, typically $b\bar{b}$ pairs. For the inert doublet model, the same exact $Z_2$ symmetry that provides the dark matter candidate forces all collider signatures to end in electroweak gauge bosons plus missing energy.

What would settle it

A dedicated ATLAS or CMS search for $p p \to h_3 \to h_1 h_2$ and $p p \to h_a \to h_b h_b$ in final states with four or six b-jets, using the Run 2 dataset, would settle the central claim: predicted rates of tens of picobarns would be visible, while the absence of an excess would exclude the benchmark regions where those rates are quoted.

Watch

Extended reading notes

Core claim

The paper's central claim is that the most promising unprobed corner of the extended scalar sector is not the already-searched resonant or Higgs-pair channels but scalar-to-scalar decays between non-SM scalars. In the $Z_2\otimes Z_2'$ two-real-scalar model, three neutral scalars mix and couple to Standard Model particles through rescaling factors that must satisfy an orthogonality relation; the measured 125 GeV scalar has a near-unity rescaling factor, yet the other two scalars can still be produced at the LHC and decay into each other. Companion benchmark scans give production rates up to approximately 60 pb for $p p \to h_3 \to h_1 h_2$ and $p p \to h_a \to h_b h_b$ at 13 TeV while satisfying perturbative unitarity, boundedness, Higgs signal-rate measurements, and current search limits. For the singlet extension and the inert doublet model, the paper concludes that viable parameter regions remain, with the inert doublet model requiring modified search strategies such as lower missing transverse energy cuts rather than entirely new final states.

Load-bearing premise

The paper's maps of which parameter points survive rely on the reliability of the computer tools and search re-interpretations used to enforce constraints; in particular, one inert-doublet exclusion comes from a leading-order recast with an estimated missing-energy cut, and the two-real-scalar rates were imported from a companion paper using a private scanner with no independent cross-check here.

Editorial extensions

If this is right

If the two-real-scalar model is realized, Run 2 data should already contain multi-b-jet events from scalar-to-scalar decays, with the largest benchmark rates reaching tens of picobarns.
The singlet extension's allowed parameter space is dominated by Higgs signal-rate measurements and direct heavy-scalar searches up to masses around 1 TeV, with the W-boson mass and coupling perturbativity cutting in at higher masses.
The inert doublet model survives all current constraints but has not been directly tested by the LHC experiments; recasts of vector-boson-fusion and monojet searches exclude only part of its parameter space, mainly the region where the dark-matter scalar is slightly off shell.
At a future $e^+e^-$ collider, lepton-plus-missing-energy final states could reveal the inert doublet model for dark scalar masses below roughly 500 GeV, with the semi-leptonic channel extending the reach toward 1 TeV.
Scalar-to-scalar signatures with final states different from the 125 GeV Higgs should be included in future search menus, since simple counting implies the existing dataset already has enough collisions to contain them if the predicted rates are correct.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the scalar-to-scalar production rates are as large as reported, the main obstacle is the absence of a dedicated search rather than luminosity; even a small signal efficiency would make these events visible in the accumulated Run 2 data.
The same asymmetric-decay mechanism could appear in other multi-scalar models, so a model-independent search for $h_a \to h_b h_b$ with four or six b-jets might be broadly useful beyond this specific benchmark model.
Lowering missing-transverse-energy thresholds in multi-lepton analyses could open up the inert doublet model's parameter space, and likely also other dark-sector scenarios with compressed mass spectra, a direct testable consequence of the recast discussion in the paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a LHCP2019 proceedings note by Tania Robens, not a fresh research paper. It does two useful things: it updates the real-singlet exclusion maps with the 2019 ATLAS/CMS di-Higgs combination limits, and it lays out the current status of the inert doublet model, including a VBF recast from her group's earlier work. The part that will get attention is Section 4: in the two-real-scalar model, scalar-to-scalar production like pp -> h3 -> h1h2 can reach O(60 pb) at 13 TeV 'while still complying with all current theoretical and experimental bounds.' That is a striking number and a good hook for experimentalists.

Credit where due: the paper is honest and clearly written. It says explicitly which figures are taken from prior papers, and it flags that the IDM VBF limit is based on an LO recast with a K-factor and hand-estimated missing transverse energy, recommending fully simulated samples. That is the right level of transparency.

The soft spot is the same one the stress-test note hits. The 60 pb rate claim is not supported inside this paper. The text says only that results came from a private version of ScannerS and refers you to the companion paper [76]. For BP4, where M3 = 125 GeV, an O(60 pb) rate means the 125 GeV state is produced almost as often as the SM Higgs and decays almost entirely to lighter scalars, not to SM fermions. That is a strong statement. It could easily be wrong if kappa_125, the branching ratios, or the treatment of 4b final states in HiggsBounds/HiggsSignals shift by even a few percent. The paper is appropriately cautious about the IDM recast but applies no equivalent caution here.

I would not call that fatal. For a proceedings write-up, it is acceptable to point to a companion paper for details, and the models themselves are not novel claims of this paper. But if this were a regular journal submission, I would ask for either an independent check of the Section 4 rates or an explicit sentence saying they are preliminary and need full-simulation cross-checks.

Who is this for? Experimental colleagues who want a quick map of what is still allowed in the singlet and inert doublet models, and a pointer to possible new search channels. They can read it in twenty minutes. It does not replace the original papers.

Recommendation: yes, send it to a serious referee if it reaches a journal; the updates are small but the claims are concrete and a referee will keep the author honest about the Section 4 uncertainty.

Referee Report

3 major / 4 minor

Summary. This proceedings contribution surveys constraints on three extended scalar sectors: the real singlet extension, the inert doublet model (IDM), and the two-real-singlet extension. The author updates the singlet model parameter space using HiggsBounds, HiggsSignals, the W-boson mass, and perturbativity constraints; recasts VBF and monojet searches for the IDM; reports CLIC projection significances for IDM scalar pair production; and presents benchmark rates for scalar-to-scalar decays pp -> h3 -> h1h2 and pp -> ha -> hbhb in the two-real-singlet model, including a BP4 point with pp -> h3 -> h1h1 rates up to about 60 pb at the 13 TeV LHC, claimed to satisfy all current theoretical and experimental bounds. The paper recommends dedicated experimental searches for these signatures.

Significance. The paper is a compact status report and a useful motivator for new LHC searches. Its strengths include the use of publicly available tools (HiggsBounds, HiggsSignals, 2HDMC, micrOmegas), the explicit caveats attached to the IDM VBF recast, and the CLIC projection results drawn from dedicated simulations. If the Section 4 rates are correct, they identify an uncovered signature with multi-picobarn production rates, which would be a genuinely useful experimental target. However, the central quantitative claim is not independently established in this manuscript: the benchmark planes and rate maps are imported from the companion paper [76] and computed with a private version of ScannerS, with no independent cross-check, no recast of the relevant multi-b-jet searches, and no uncertainty estimate. The paper's strongest recommendation therefore inherits the reliability of an external, non-public implementation.

major comments (3)

[Section 4, Figure 6 (BP4)] The O(60 pb) rate for pp -> h3 -> h1h1 is the load-bearing quantitative claim of the paper, but it is not supported within this manuscript. The text states that "results have been obtained using a private version of the ScannerS framework," and the benchmark rates are taken from the companion paper [76] without independent verification. Since BP4 has M3 = 125 GeV, a 60 pb rate requires near-SM h3 production and near-unity h3 -> h1h1 branching; small corrections in kappa_125, in the branching ratio, or in the treatment of the 4b final state by HiggsBounds/HiggsSignals could all change the conclusion. The authors should provide an independent cross-check, for example a public model file, a comparison of the cross-section normalization with an established tool, and a recast of existing multi-b resonance searches, or should explicitly re-label the claim as an inherited result from [76] with the associated uncertainty.
[Section 3.1, Figure 4] The IDM viability conclusion depends on the VBF recast, which the author correctly describes as a leading-order calculation with a K-factor and hand-estimated missing transverse energy. The caveat is stated, but its practical impact is not quantified. Since the surviving region labelled "Allowed by Dark Matter + VBF Constr." in Figure 4 is defined by this approximate recast, the paper should state an estimated uncertainty on the recast boundary or identify which parts of the surviving parameter space are robust to a 10-20% change in the signal efficiency or to offshell/interference effects.
[Section 4, text after Eq. (4.4)] The claim that scalar-to-scalar decays with all final-state scalars different from 125 GeV "have not yet been fully explored" is too strong without a more systematic check of existing searches. The paper mentions only the ATLAS WWWW search [79] as covering a small region of the h3 -> h2h2 plane, but does not discuss constraints from existing 4b, bbtautau, or bbll resonance searches that can be sensitive to the benchmark final states. Please specify which existing searches have been explicitly checked for BPs 1, 3, 4, and 5, and why they do not exclude the high-rate regions shown in Figure 6.

minor comments (4)

[General] There are several typographical errors, including "goverend" in Section 3.2, "signatures has been" in Section 4, and "Mh & Mh/2" in the caption of Figure 4; these should be corrected to read "governed," "signatures have been," and "MH & Mh/2," respectively.
[Figure 5] The axis label "M_H + mA" should be "MA + MH", and the notation "S+B/S = S/sqrt(S+B)" is not defined explicitly in the text; please add a sentence defining the significance variable used in the plots.
[References] Several references are given only as arXiv identifiers without journal or proceedings information (for example [30], [61], [62], and [79]); adding full citation details would improve the manuscript's usability.
[Figure 3] The left and right panels of Figure 3 are reproduced from other works and are not described in enough detail for the reader to understand the scan ranges or the meaning of the grey and red points; please expand the caption or refer more explicitly to the defining equations and parameter ranges.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the constraint inputs are external, and the Section 4 rates, although imported from a same-author companion paper via a private ScannerS build, are externally falsifiable model scan outputs rather than definitional reductions.

full rationale

The paper's constraint maps are anchored in external data and public tools: HiggsBounds-5.4.0, HiggsSignals-2.3.0, micrOmegas, 2HDMC, ATLAS/CMS search combinations, XENON and relic-density inputs. Section 2's maximal pp->h2->h1h1 curves are scans of the singlet model against those external limits; the W-mass line is a precision-observable calculation, not a fit to the plotted rate. Section 3's IDM discussion relies on the VBF recast of [34], and the paper itself flags the limitation: 'This emphasizes the importance of comparing fully simulated samples, including all offshell and interference effects, with current limits.' That is an acknowledged approximation, not circularity. Section 4's central claim, rates up to O(60 pb) for scalar-to-scalar decays while satisfying all constraints, is not derived in this paper; it is imported from the companion paper [76] (Robens, Stefaniak, Wittbrodt) and from 'a private version of the ScannerS framework.' This is a load-bearing self-citation and a transparency/verification weakness, and the skeptical concern that no independent check is provided is legitimate. However, it is not circular in the defined sense: the benchmark planes are model scans subject to external constraints, and the resulting signal rates are falsifiable by LHC searches; the paper does not define any parameter in terms of the predicted rate, nor rename a fitted quantity as a prediction, nor invoke a uniqueness theorem from the authors' prior work. No equation in the paper reduces by construction to an input. Hence the circularity score is 0, with the Section 4 reproducibility caveat noted separately.

Assumptions & free parameters 4 free parameters · 5 assumptions · 3 invented entities

This proceedings paper introduces no new entities, free parameters, or axioms of its own; it reports constraints on three models inherited from prior literature. The ledger records what the plots depend on. The model parameters are scanned or fixed by hand (tan beta = 0.1 in Fig. 1; five IDM parameters; six benchmark planes from [76]); they are not fitted to data in this paper. The load-bearing axioms are the assumed validity of the three model frameworks, the correctness of the public tool implementations, and the faithfulness of the recast in [34]. All scalar states listed are inherited entities with no direct observational evidence, hence independent_evidence is false for each. The ledger is deliberately conservative: the paper's contribution is the constraint survey, and the survey's output is directly determined by these inherited inputs.

free parameters (4)

singlet model: scalar masses M_H, M_h and mixing angle sin alpha
Scanned parameters of the Z2-symmetric singlet model (Eq. 2.1) used for Figs. 1 and 2; M_h is fixed to 125 GeV and the pairs (M_H, sin alpha) are scanned.
singlet model: tan beta = 0.1 (fixed in Fig. 1)
Fixed by hand to 0.1 for the constraint survey in Fig. 1, as stated in the caption; the constraint picture may shift for other values.
IDM parameters: M_H, M_A, M_H+-, lambda2, lambda345
Five free parameters of the Inert Doublet Model (Eq. 3.2) scanned in [33] and [34]; benchmark points in Figs. 3-5 are taken from those papers.
Two-singlet model: benchmark plane masses and couplings (BP1, BP3, BP4, BP5)
Benchmark planes defined in [76] and used for the rate predictions in Fig. 6; the parameter definitions and scan procedure are not given in this paper.

assumptions (5)

domain assumption The Z2-symmetric singlet potential of Eq. (2.1), with both fields acquiring vevs, is a valid framework for extended scalar sector studies.
Section 2 adopts this model from [5,6] without re-deriving its viability; the mixing angle parametrization and the definition of tan beta follow from that prior work.
domain assumption The Inert Doublet Model with the exact Z2 symmetry of Eq. (3.1) and H as the stable dark matter candidate is the correct interpretation of the second doublet.
Section 3.1 assumes the Z2 assignments and treats H as DM; relic density and direct detection constraints from micrOmegas and XENON are then used to restrict the parameter space.
domain assumption HiggsBounds 5.4.0 and HiggsSignals 2.3.0 correctly encode the relevant ATLAS and CMS searches and signal-rate measurements.
Section 1 states these public tools are used for all exclusion and signal-strength results; errors in their internal implementation of experimental likelihoods would propagate into every constraint plot.
domain assumption The theoretical admissibility conditions (perturbativity, boundedness from below, perturbative unitarity) as implemented in the scans define the allowed parameter space.
Figures 1, 2, and 6 show contours labelled 'lambda1 perturbativity', 'Unitarity', and 'Boundedness', but the precise criteria are not stated in this paper.
domain assumption The recast of the CMS VBF invisible-Higgs search performed in [34] is a faithful approximation of the experimental analysis.
Section 3.1 uses this recast to exclude an upper triangle in the (M_H, lambda345) plane; the author notes offshell and interference effects were not fully simulated, so the validity of the approximation is load-bearing.

invented entities (3)

Real singlet scalar S (mass eigenstates h, H)
purpose: Extends the SM scalar sector; produces universal suppression of SM couplings by sin alpha and a heavy H -> hh resonance.
Inherited from [5,6]; not introduced by this paper. No direct observation; only indirect constraints are presented.
Inert doublet scalars H, A, H+-
purpose: Provide the dark matter candidate H and signatures with electroweak gauge bosons plus missing transverse energy.
Inherited from [7-9]; no direct observation. The dark matter interpretation itself is assumed as part of the model.
Two real singlet scalars S and X (mass eigenstates h1, h2, h3)
purpose: Enable asymmetric and symmetric scalar-to-scalar decays such as pp -> h3 -> h1h2.
Inherited from [73-76]; no direct observation. The predicted rates are falsifiable by future LHC multi-b searches, but no observational handle outside the model is provided here.

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Cite this review

Pith. "Pith review of Investigating extended scalar sectors at current and future colliders." pith.science (2026). https://pith.science/paper/IZR72DBZ

@misc{pith2026190810809,
  author       = {Pith},
  title        = {Pith review of: Investigating extended scalar sectors at current and future colliders},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IZR72DBZ}},
  note         = {Machine review of arXiv:1908.10809}
}

read the original abstract

In this work, I briefly report on constraints that can be obtained on new physics models that extend the scalar sector of the Standard Model (SM) of particle physics at the LHC. I concentrate on a few simple examples which serve to demonstrate advantages as well as possible drawbacks of current experimental searches, and comment on the discovery prospects of such models at future colliders.

Figures

Figures reproduced from arXiv: 1908.10809 by the authors.

**Figure 1.** Current constraints on the parameter space of the Higgs singlet extension. Shown are limits from the W-boson mass as a precision observable [21] (solid, red), direct searches as implemented in HiggsBounds (green, dashed), limits from signal strength measurements as implemented in HiggsSignals (magenta, dashed), as well as limits from perturbativity of λ1. tanβ has been fixed to 0.1. This figure corresponds to an up… view at source ↗

**Figure 2.** Maximal allowed pp → h2 → h1h1 signal rate at the 13 TeV LHC in the softly-broken Z2- symmetric case. Shown are values after applying (red solid) all constraints and (blue dotted) only constraints at the electroweak (EW) scale. For comparison we include the current strongest cross section limit (at 95% CL), obtained from the combination of various CMS h2 → h1h1 searches at 13 TeV with up to 36 fb−1 of data [28] (lef… view at source ↗

**Figure 3.** Allowed parameter space in the IDM. Left: Allowed parameter range in mass differences from the generic scan presented in [33], with the figure taken from that reference. Benchmark points chosen in that reference are displayed in red. Right: allowed parameter region for the case that MH ≤ 100GeV, with allowed parameter points displayed in red. The shape for MH ≤ Mh/2 is determined by signal strength measurements. Dar… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Results of the recast of the Inert Doublet Model, presented in [34]. Left: Constraints on the parameter space in the (MH, λ345) plane taking all theoretical and experimental constraints into account. Recasts of VBF [56] and monojet [57,58] searches are also shown. For …

**Figure 5.** Figure 5: Significances obtained for e + e − → ``0+E/⊥ final state within the IDM for various center-of-mass energies, resulting from dedicated studies presented in [59]. Left column: significances in the ``0 ≡ µ +µ − channel, with major production mode via HA production. Top: S…

**Figure 6.** Figure 6: Signal rate predictions for various benchmark planes suggested in [76], at the 13 TeV LHC. Regions forbidden by specific theoretical or experimental constraints are indicated accordingly. Top left: BP1, where M3 = 125GeV. Production rates reach ∼ 3 pb, with dominant b…

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