Search for Invisibly Decaying Light Scalars at the FCC-ee

Aman Desai; Tania Robens

REVIEW 3 major objections 3 minor 31 references

At the FCC-ee, invisibly decaying light scalars produced with a Z boson could be discovered up to about 80 GeV, with expected cross-section limits as low as 10^-2 fb.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 11:12 UTC pith:JC7DXA4G

load-bearing objection Solid FCC-ee sensitivity study with a public model and clean analysis chain, but the benchmark parameters contradict the paper's own mixing equations, so the discovery-reach claim is unsupported as written. the 3 major comments →

arxiv 2606.16284 v1 pith:JC7DXA4G submitted 2026-06-15 hep-ph

Search for Invisibly Decaying Light Scalars at the FCC-ee

Aman Desai , Tania Robens This is my paper

classification hep-ph

keywords light scalarinvisible decayFCC-eeHiggs portalscalar singletdark matterrecoil masscollider sensitivity

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to show that a future electron-positron collider operating at 240 GeV with 10.8 inverse attobarns—the proposed FCC-ee—can search for new light scalar particles that decay invisibly. These scalars are produced together with a Z boson, which is required to decay to a quark-antiquark pair; the scalar itself is inferred from missing momentum and the recoil mass of the Z. Using a simplified model with a scalar singlet and a dark-matter candidate, the authors simulate signal and Standard Model background, then apply event selections and a boosted-decision-tree multivariate classifier. They report expected 95% CL upper limits on the production cross-section times invisible branching fraction of order 10^-2–10^-1 fb below the Z mass and 0.1–1 fb between 80 and 120 GeV, and conclude that scalars up to 80 GeV lie within discovery reach depending on the scalar–Higgs mixing angle. If right, this gives a concrete, model-lean target for the physics programme of a Higgs factory.

Core claim

The central claim is that the e+e- -> Z h1 (h1 -> invisible) process at sqrt(s) = 240 GeV and L = 10.8 ab^-1 can be measured with expected 95% CL upper limits on sigma(e+e- -> q qbar h1) x B(h1 -> invisible) of roughly 10^-2–10^-1 fb for scalar masses below the Z mass and 0.1–1 fb in the 80–120 GeV range. The analysis uses a singlet-scalar toy model in which a new scalar h1 mixes with the 125 GeV Higgs boson and decays invisibly to a 5 GeV dark-matter scalar. Event generation includes interference between the new scalar and the Standard Model Higgs, which matters when their masses are close. With the benchmark mixing parameter sin alpha = 0.985, the expected significance exceeds 5-sigma for

What carries the argument

The load-bearing observable is the Z-boson recoil mass, M_recoil = sqrt(s + m_jj^2 - 2 E_jj sqrt(s)), built from the hadronic Z decay; a true invisible scalar of mass M creates a peak in this variable. The analysis combines preselection cuts on the Z mass, jet topology, and missing momentum with a boosted-decision-tree classifier trained on jet kinematics and the recoil mass, then converts the classifier output into expected upper limits using an asymptotic profile-likelihood treatment with a 10% background uncertainty. The underlying model is a scalar singlet mixing with the Standard Model Higgs (mixing angle alpha), with the new scalar decaying invisibly to a dark-matter candidate, and the

Load-bearing premise

The reach numbers assume the benchmark scalar model is physically viable—in particular, that a 125 GeV state with a roughly 6.9 MeV width and about 7.5% invisible-plus-cascade branching is the observed Higgs boson, and that the low-mass, strongly mixed scalar states used for the discovery claim are not already ruled out by earlier collider searches.

What would settle it

A decisive check is to take the LEP-era decay-mode-independent bounds on e+e- -> Z S (S -> invisible) and evaluate them at the benchmark masses and couplings: if those bounds exclude the benchmark production rates of roughly 13–20 fb after scaling to LEP center-of-mass energies, the claimed discovery reach is already excluded. Independently, compare the assumed Higgs total width of about 6.9 MeV with the measured total width of the 125 GeV Higgs, which is far smaller; that comparison alone would settle whether the benchmark model is viable.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

At 240 GeV and 10.8 ab^-1, the FCC-ee could exclude invisible-scalar production cross-sections down to about 10^-2–10^-1 fb for scalar masses below the Z mass, and 0.1–1 fb in the 80–120 GeV range.
For scalar–Higgs mixing angles near 0.985, the expected significance exceeds 5σ for masses up to about 80 GeV, making discovery plausible in a single run.
The reported upper limits are nearly independent of the mixing angle over 0.973–0.995, so they can serve as approximate model-independent constraints on this production topology.
The analysis includes interference between the new scalar and the Standard Model Higgs, so its sensitivity statement remains meaningful where the two resonances overlap near 125 GeV.
For low masses (15–60 GeV), the scalar peak in the recoil-mass distribution is well separated from backgrounds, which is why the strongest sensitivity appears at the low end of the mass range.

Where Pith is reading between the lines

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

Editorially: the limit curves, expressed as sigma x B, can be rescaled by any model's production cross-section and branching fraction, so the sensitivity numbers carry over to dark-photon, axion-like, or hidden-sector scenarios with the same Z-associated topology—even though the paper's benchmark is a singlet-plus-dark-matter toy model.
Editorially: a natural extension is to search for the scalar's visible decays using the same recoil-mass spectrum; the present invisible analysis's strong low-mass reach suggests an analogous visible search would extend the programme without needing additional luminosity.
Editorially: FCC-ee's proposed high-luminosity run at the Z pole would multiply Z-associated production rates, so recasting this analysis there could push the cross-section reach below 10^-2 fb for low-mass scalars.
Editorially: the sensitivity dips near the Z and Higgs masses arise from ZZ and ZH backgrounds; a future analysis with a finer background decomposition or alternative jet definitions might recover some of the lost sensitivity, but that is a suggestion beyond the paper's claims.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Solid FCC-ee sensitivity study with a public model and clean analysis chain, but the benchmark parameters contradict the paper's own mixing equations, so the discovery-reach claim is unsupported as written.

read the letter

Here's the short version: this is a competent FCC-ee sensitivity study with a public model and a clean analysis chain, but the benchmark parameters as written are internally inconsistent, and the discovery-reach claim should not be taken at face value. The model-independent limit curves may survive a fix; the significance curves probably won't.

What's actually new: the authors ship a FeynRules/UFO implementation of a singlet-plus-DM scalar model, generate e+e−→Z(qq)+χχ samples with interference with the SM Higgs included, use the Winter2023 official backgrounds with ISR/FSR and beam spread, apply a BDT in the FCCAnalyses framework, and produce expected 95% CL limits via CMS Combine. The public model and the explicit interference treatment are useful for future studies, and the limit-setting machinery is standard and looks sound.

The problem is the benchmark. Eq. (3) with sinα=0.985 makes h1 mostly doublet (component 0.985) and h2 mostly singlet (component 0.173). Yet h2 is identified as the SM Higgs and Table I quotes Γ_h2≈6.85 MeV with ~7.5% BSM width. That width requires a near-SM doublet component, not 0.173. The production cross-sections in Table I (13–20 fb) are also an order of magnitude too small for a mostly-doublet h1; they look like the numbers you'd get with sinα≈0.17. So there is a convention mismatch between the stated parameters and the implementation. That mismatch is load-bearing: the significances in Fig. 6 and the 'discovery up to 80 GeV' conclusion depend directly on these cross-sections. I don't see a way around that without a corrected scan.

Second, the paper itself says it does not impose all constraints, and no LEP/OPAL bounds are overlaid for low-mass, large-mixing h1. A mostly-doublet h1 in this mass range would likely already be excluded, so the abstract's claim that 'existing experimental constraints do not yet exclude these states' is not established. The paper needs an explicit comparison with direct searches.

The limit curves in Fig. 7 are model-independent in the sense that they quote σ×BR limits, and those could stand after renormalizing to a consistent benchmark. But as written, I would treat the discovery reach and the absolute normalizations with serious caution.

This paper is for people working on FCC-ee Higgs-factory projections and on singlet/DM scalar benchmarks. It deserves a serious referee, but the referee should ask for a corrected benchmark, a full constraint overlay, and a rerun of the significance curves.

Referee Report

3 major / 3 minor

Summary. The paper presents a simulation-based projection for the process e+e− → Z(→jj) h1, with h1 decaying invisibly, at the FCC-ee (√s = 240 GeV, L = 10.8 ab−1). The authors introduce a simplified model of a real scalar singlet mixed with the SM Higgs plus a scalar dark-matter candidate, generate signal and background events with MadGraph/Pythia/Delphes using the IDEA detector parametrization, and analyze them with a cut-based strategy and an XGBoost BDT. Expected significances are computed with the Asimov formula and expected 95% CL upper limits on σ(e+e−→Zh1) × B(h1→invisible) are derived with CMS Combine. The main claims are: sensitivities of ~10−2–10−1 fb below the Z mass, 0.1–1 fb in the 80–120 GeV range, and discovery reach for scalar masses up to 80 GeV depending on the mixing angle.

Significance. If the results are correct, the paper would provide a useful, technically detailed projection for a key FCC-ee search channel. The analysis chain is standard and largely reproducible: the UFO model is publicly available, the event generation uses well-established tools, the BDT is carefully described, and the limit-setting uses the CMS Combine machinery. The treatment of h1–h2 interference is a positive feature. There is no fitted-to-target circularity. However, the benchmark model on which the signal normalization and the discovery-reach claim rest is internally inconsistent with the stated mixing convention. This undermines the central quantitative claims as currently presented, and the lack of any LEP/OPAL constraint overlay leaves the statement that 'existing experimental constraints do not yet exclude these states' unsupported.

major comments (3)

[II, Eq. (3), Table I] The benchmark is internally inconsistent with the mixing convention. Equation (3) gives h2 = −sinα φS + cosα φ, so with sinα = 0.985, cosα ≈ 0.173 and h2 has a doublet component of only cos^2α ≈ 0.03. Its SM-like width would then be ≈ 0.03 × 4.1 MeV ≈ 0.12 MeV. Adding the BSM contribution implied by Table I (B_cascade ≈ 7.5% of Γ_h2 = 6.85 MeV, i.e. ≈ 0.51 MeV) gives a total width ≈ 0.6 MeV, not 6.85 MeV. Conversely, to obtain Γ_h2 ≈ 6.85 MeV with only 7.5% BSM width requires SM-like partial widths summing to ≈ 6.3 MeV, which is impossible for cos^2α = 0.03. Similarly, with sinα = 0.985, h1 is mostly doublet (component ≈ 0.985), so σ(e+e−→Zh1) at √s = 240 GeV should be of order 0.97 × σ_SM(ZH) × BR(Z→jj), i.e. roughly 100 fb, whereas Table I reports 13–20 fb. The quoted cross-sections are of the size expected for a mostly-singlet h1 (doublet component ≈ 0.17). Thus the parameter input an
[II, §VI, abstract] The paper does not apply LEP/OPAL constraints, despite citing OPAL [5] and stating in §II that 'we do not impose all constraints'. With the stated sinα = 0.985, h1 is mostly doublet, so LEP e+e−→Zh1 searches, including invisible decays, would be directly relevant and likely exclude most of the 15–80 GeV mass range where the paper claims discovery reach. The abstract statement that 'existing experimental constraints do not yet exclude these states' is therefore not established. The authors should either overlay the relevant LEP limits on the benchmark points or demonstrate explicitly that the surviving parameter space still yields the quoted cross-sections and significances.
[IV, Fig. 6] The significance curves in Fig. 6 are computed using the cross-sections from Table I, which are the same cross-sections that are inconsistent with the mixing convention in Eq. (3). Even if the kinematic shapes used for the BDT are approximately model-independent, the absolute signal normalization is not. After correcting the mixing convention, the signal yields, and therefore the significances and the 'up to 80 GeV discovery' conclusion, will change. The model-independent upper-limit part of the paper may survive, but the discovery-reach claim needs to be re-derived with a physically consistent benchmark.

minor comments (3)

[Table II] The units in Table II appear inconsistent for the rows labeled 'ννH(→ ...)': for example, 'e+e−→ννH(→bb)' is listed as 26.7 pb, which is three orders of magnitude larger than the expected ZH production with Z→νν and H→bb (of order 20–30 fb). The numbers appear to be in fb rather than pb. Please correct the table header or the values, and verify that the analysis uses the correct normalizations.
[Fig. 2] The caption for Fig. 2 refers to 'the simulation for e+e−→Z(jj)h1(χχ) with sinα = 0.985' in black dotted lines, while the text says this is obtained using h1 mediation only. Please clarify whether this curve is generated with the full interference or with only the h1 propagator, since the two are compared.
[IV, Eq. (12)] For M_S = 25 GeV the pmiss threshold in Eq. (12) is 10 GeV, which is the same as the preselection cut in Table III. This makes the additional cut redundant for that mass point. Check whether the threshold is intentionally 10 GeV or should be a slightly larger value.

Circularity Check

0 steps flagged

No significant circularity: the expected limits are extracted from simulated signal/background samples via a profile-likelihood fit; benchmark inputs are not fitted to the claimed limit.

full rationale

The central result is an expected-upper-limit projection, not a parameter extraction. Signal events are generated from a toy model (Eq. 1) with fixed inputs (sinα=0.985, Mχ=5 GeV, M2=125 GeV, v=246 GeV), with benchmark points in Table I selected to satisfy external constraints (B(h2→invisible)<10%, Γ_h2∈[4,8] MeV, perturbativity |λi|≤4π). The 95% CL limits are then obtained with the CMS Combine AsymptoticLimits machinery from MVA score distributions, with signal normalized to a reference value, so the quoted σ×B upper limits are statistically extracted rather than equal to an input. The 'discovery reach' statements are model-dependent projections, which is standard and not circular. Self-citations (e.g., [17], [26]) motivate the toy model and one benchmark value, but the analysis is not forced by them: the mixing angle is varied (sinα=0.973, 0.985, 0.995) and the limits are shown to be largely independent of it. The paper explicitly notes in Section II that 'we do not impose all constraints that would in principle be viable for a UV complete theory'; this admitted limitation, and any internal inconsistency in the benchmark, are correctness/external-constraint concerns rather than circularity—no equation is defined in terms of the target and no fitted parameter is renamed as a prediction.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 2 invented entities

The central claim rests on a toy model whose parameters are partly chosen by hand and partly scanned to satisfy constraints. The largest burden is the assumption that the benchmark points are physically viable despite the sin α = 0.985/h2-as-SM-Higgs tension and the absence of LEP/LHC exclusion overlays. The statistical tools themselves are standard and do not add free parameters beyond the stated systematic assumptions.

free parameters (5)

Mixing angle sin α = 0.985 (varied 0.973, 0.995)
Hand-set mixing angle 'motivated by [26]'; controls h1 coupling to Z and h1-h2 interference, and determines the absolute signal cross-section used for the discovery-reach claim.
Dark matter mass Mχ = 5 GeV
Fixed by hand; not scanned or justified by external constraints.
Portal coupling λχ = per-benchmark values, e.g. -5.0e-4 for 15-55 GeV and -2.5e-3 for 65-120 GeV (Table I)
Scanned over [-0.1, -1e-6] ∪ [1e-6, 0.1] to satisfy Br(h2→inv) and width constraints; sets h1→χχ width and benchmark cross-section.
Singlet VEV vS = per-benchmark values, e.g. 2936-8514 GeV (Table I)
Scanned over [50, 5×10^5] GeV; enters scalar widths and cross-sections.
pmiss cut thresholds = 10-36 GeV depending on MS (Eq. 12)
Analysis cuts optimized per mass hypothesis; not derived from data, but affects expected significance.

axioms (5)

domain assumption Eq. (1) scalar potential with a softly broken Z2 and the specified mixing matrix is a physical realization of a light scalar plus dark matter model.
Underpins all signal MC; no direct evidence for such a scalar sector is provided.
ad hoc to paper h2 in Eq. (3) can be identified with the observed 125 GeV Higgs while sin α = 0.985.
With sin α = 0.985, h2's doublet component is cos α ≈ 0.17, so h2 is not SM-like; the paper does not reconcile this with LHC Higgs signal-strength measurements.
domain assumption Existing experimental constraints (OPAL, LEP, LHC) do not exclude the scanned benchmark points.
The paper claims this in the abstract/introduction but plots no existing-exclusion overlay; LEP bounds on light Higgs-like states may rule out large mixing.
domain assumption The 10% background systematic and 1% luminosity uncertainties are representative.
Used for Asimov significance and limits; no data-driven validation at FCC-ee is yet possible.
domain assumption Narrow-width approximation with Γ_h1/M1 < 15%.
Applied to justify on-shell scalar production and simple recoil-mass reconstruction.

invented entities (2)

Light scalar singlet h1 no independent evidence
purpose: Signal state, e+e−→Z h1, h1→χχ
Generic BSM entity; not observed and no external handle is supplied in this paper beyond a projected sensitivity.
Scalar dark matter candidate χ no independent evidence
purpose: Invisible decay product of h1/h2; gives the missing-momentum signature
No direct-detection, relic-density, or collider handle outside this paper; mass fixed at 5 GeV by hand.

pith-pipeline@v1.3.0-alltime-deepseek · 13690 in / 19430 out tokens · 219877 ms · 2026-08-02T11:12:26.560841+00:00 · methodology

0 comments

read the original abstract

We investigate the production of invisibly decaying light scalars in association with hadronically decaying $Z$ bosons at the Future Circular Collider-ee at a centre-of-mass energy $\sqrt{s}=240$ GeV. Several new physics models predict the existence of these low-mass scalar states, while the existing experimental constraints do not yet exclude these states. We study the low-mass scalar based on a simplified extension of the Standard Model, introducing an additional scalar singlet and a scalar dark matter candidate. The analysis is performed for a set of new scalars with mass in the range $(15, 120)$ GeV, by employing a selection-based strategy complemented with Multivariate Analysis techniques to discriminate the signal from background. The expected upper limits on the production cross-section times the branching fraction of the new scalars decaying invisibly are evaluated as a function of the scalar mass. We find that sensitivities of $\sim 10^{-2}$--$10^{-1}$~fb are achievable for scalar masses below the $Z$ boson mass, while sensitivities of $0.1$--$1$~fb are obtained in the mass range 80--120 \GeV. Depending on the mixing angle, novel scalars with masses up to 80 \GeV are within discovery reach.

Figures

Figures reproduced from arXiv: 2606.16284 by Aman Desai, Tania Robens.

**Figure 2.** Figure 2: FIG. 2: The distribution of the recoil mass considering three different mixing angles, [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Distributions of (a) leading jet [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: An example of the ROC curve for [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: MVA score distributions for signal samples at different scalar masses with [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Expected signal significance (Asimov) for the [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Expected 95% CL upper limits on [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: Expected 95% CL upper limits on [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

discussion (0)

Reference graph

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