Searching for long-lived dark scalars at the FCC-ee

Axel Gall\'en; Giulia Ripellino; Magdalena Vande Voorde; Rebeca Gonzalez Suarez

REVIEW 3 major objections 3 minor 2 cited by

Searching for long-lived dark scalars at the FCC-ee

T0 review · 3 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A background-free selection based on a Z-like lepton pair plus two displaced vertices can probe Higgs decays to long-lived dark scalars at branching ratios down to $10^{-4}$ for lifetimes near 1 m.

desk verdict A clean, internally consistent FCC-ee sensitivity projection for displaced dark scalar decays; the reach numbers are plausible but rest on a fast-simulation vertexing efficiency that needs a full Geant4 check before being treated as quantitative. read the letter →

arxiv 2412.10141 v2 pith:BN6UX4XP submitted 2024-12-13 hep-ex hep-ph

Giulia Ripellino , Magdalena Vande Voorde , Axel Gallén , Rebeca Gonzalez Suarez This is my paper · ORCID

classification hep-exhep-ph

keywords long-liveddarkscalarsexoticHiggsdecaysdisplacedverticesFCC-eeIDEAdetectorconceptportalZHproductionbackground-freesearch

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 paper claims that a dedicated search for displaced vertices at the FCC-ee can probe exotic Higgs decays into pairs of long-lived dark scalars with branching ratios down to $10^{-4}$, covering dark scalar masses from 20 to 60 GeV and mean proper lifetimes $c\tau$ from roughly 10 mm to 10 m. The signal is $Zh$ production at $\sqrt{s}=240$ GeV with the $Z$ decaying leptonically and the Higgs decaying to two dark scalars that each decay to $b\bar{b}$, so the final state contains at least two displaced vertices. Using a fast, parametrized simulation of the IDEA detector concept and an event selection that requires a Z-like lepton pair plus two or more displaced vertices, the authors find zero Standard Model background in the simulated samples. This is the first sensitivity estimate for exotic Higgs decays at FCC-ee with the IDEA detector concept, and it suggests a discovery-level channel complementary to LHC searches.

What carries the argument

The load-bearing mechanism is the displaced-vertex selection built on non-primary tracks. Tracks with $p_T>1$ GeV and $|d_0|>2$ mm seed a secondary-vertex finder; vertices are required to have at least three tracks, a charged invariant mass above 2 GeV, and to lie within the 2 m radial tracker volume. The $|d_0|$ cut is what suppresses heavy-flavour background, the mass and multiplicity cuts reject random track crossings, and the final requirement of at least two such vertices, together with a $Z$-mass lepton pair, eliminates all simulated Standard Model processes.

What would settle it

Run a full detector simulation of $e^+e^-\to Zh\to l^+l^-b\bar{b}b\bar{b}$ for the 50 GeV, $3\times10^{-7}$ signal point and for the dominant $Zh$, $ZZ$, and $WW$ backgrounds, and count displaced vertices satisfying $N_{\rm trk}\ge3$ and $m_{\rm ch}>2$ GeV; if the reconstructed-vertex rate or the zero-background result changes by more than the statistical uncertainty, the claimed $10^{-4}$ branching-ratio reach would need revision.

Watch

Extended reading notes

Core claim

The central claim is that a background-free search for $h \to ss \to b\bar{b}b\bar{b}$ is achievable at the FCC-ee. The selection starts from events with exactly two opposite-charge, same-flavour leptons whose invariant mass lies between 70 and 110 GeV, then requires at least two reconstructed displaced vertices satisfying track multiplicity $N_{\rm trk}\ge 3$ and charged invariant mass $m_{\rm ch}>2$ GeV. With this selection, all $Zh$, $ZZ$, and $WW$ background events in the simulation are removed, while a grid of signal samples with $m_s$ between 20 and 60 GeV and $\sin\theta$ between $10^{-7}$ and $10^{-5}$ retains up to 32% acceptance. The authors argue that rescaling to lower coupling would allow probing $\text{BR}(h\to ss)$ below $10^{-4}$ at $c\tau\approx 1$ m, with the best point (50 GeV, $3\times10^{-7}$) giving 3.3 selected events at a branching ratio of $9\times10^{-5}$.

Load-bearing premise

The search assumes the fast, parametrized simulation of the IDEA detector reconstructs displaced vertices at radii up to two metres with realistic efficiency and resolution, a point that is not checked against a full detector simulation.

Editorial extensions

If this is right

At $\kappa=0.0002$, the 50 GeV, $3\times10^{-7}$ sample corresponds to $\text{BR}(h\to ss)=9\times10^{-5}$ and gives about 3.3 selected events, so the search could realistically probe branching ratios below $10^{-4}$.
Zero background in simulation means discovery would be possible for any signal point with at least three selected events.
The selection covers $m_s$ from 20 to 60 GeV and $c\tau$ from about 10 mm to 10 m; the edges lose sensitivity because decays occur inside 2 mm or beyond 2 m.
The 50 GeV, $3\times10^{-7}$ point has the highest acceptance, about 32%, since 99% of its dark scalars decay inside the reconstructible tracker volume.

Reading between the lines

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

If the background-free behaviour persists with larger Monte Carlo statistics and a full detector simulation, the same two-displaced-vertex selection could be applied to other long-lived decays from exotic Higgs decays, such as charm or tau final states, by retuning the vertex mass and track multiplicity cuts.
The 2 m radial reach of the tracker sets a natural upper limit on the lifetime probed; adding timing information or an outer decay volume would extend sensitivity beyond $c\tau\sim10$ m.
Combining the ZH run with other Higgs production modes at FCC-ee, such as WW fusion, could improve the branching-ratio reach or cover additional mass-lifetime combinations beyond the grid studied here.

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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

Quick take: this is a clean, well-documented sensitivity projection, and the first with the IDEA detector concept in the common FCC framework. The central number — sensitivity to BR(h→ss) around 1e-4 for cτ≈1 m at 10.8 ab⁻¹ — is plausible as a planning estimate, not as a sharp discovery claim.

What's new: prior LLP work at lepton colliders (Alipour-Fard et al.) used different detector assumptions; this paper gives the first IDEA-specific study, with a full chain from MadGraph/Pythia through Delphes and LCFIPlus in FCCAnalyses. The background samples are sizable (hundreds of millions of events), the event selection is well motivated (Z-tagged dilepton plus ≥2 displaced vertices), and the acceptance tables are useful. The paper is also honest: it notes the need for larger background MC and shows the radial DV distributions, which look physically sensible.

Soft spots, in proportion. The 'discovery' threshold of three events is statistically weak — about 2σ in a zero-background counting experiment. For a projection this is common, but the shaded reach region should not be read as a real 5σ claim. The zero-background statement itself is based on finite MC; the 33M Zh / 56M ZZ / 373M WW events give good coverage, but after all cuts zero events doesn't mean the background is exactly zero. More importantly, the signal-side vertexing efficiency comes from a parametrized Delphes simulation of the IDEA tracker. The cuts (|d0|>2 mm seeds, ≥3 tracks, m_ch>2 GeV, DV radius <2 m) are exactly where pattern recognition and impact-parameter resolution matter most, and Delphes cannot model those with full fidelity. A factor-of-two change in signal efficiency would shift the 1e-4 reach noticeably. The paper flags its own limitation on the background side but does not validate the signal-side vertexing against Geant4. That's a validation gap, not an internal inconsistency; I don't see circularity or anything contrived in the selection.

Bottom line: for FCC-ee physics-case people and LLP hunters, this is a useful, citable study. It deserves a serious referee — the analysis is reproducible in structure, the limitations are mostly stated, and a referee's main job would be to push on the DV-efficiency question and the statistical definition of reach. I'd be happy to see it published after those points are either addressed or clearly caveated. Recommend: send to peer review.

Referee Report

3 major / 3 minor

Summary. This paper presents a fast-simulation sensitivity study for long-lived dark scalars produced in exotic Higgs decays at the proposed FCC-ee collider. Signal events are Zh with Z->ll and h->ss, with each s decaying to b bbar; the final state is selected by requiring a Z-like lepton pair and at least two displaced vertices reconstructed with the IDEA detector concept in Delphes. The analysis uses the FCCAnalyses framework and LCFIPlus-based secondary vertex finding with a custom track selection (|d0|>2 mm, N_trk>=3, m_ch>2 GeV). The authors report zero Standard Model background after the final selection and estimate sensitivity to BR(h->ss) as low as about 1e-4 for c tau around 1 m, based on rescaling a representative signal point from kappa=0.0007 to kappa=0.0002 and requiring three selected events.

Significance. The paper is a well-documented and internally consistent sensitivity projection for a relevant LLP signature at FCC-ee, using the common FCC software stack. Its strengths include the public simulation pipeline, clear event-count tables at each selection stage, and a straightforward branching-ratio rescaling argument. If the projected reach survives the validation concerns below, the result would be a useful benchmark for the FCC-ee physics program and for future detector-concept studies. The analysis also provides concrete insight into the role of track-impact-parameter and vertexing performance for displaced vertices in the IDEA tracker.

major comments (3)

[Section 6] The sentence "The event selection reduces the background to zero and discovery is therefore possible for any signal point with at least three selected events" conflates discovery with exclusion. In a zero-background counting experiment, observing three events corresponds to a 95% confidence-level upper limit on the signal mean (Poisson: 2.996 events), not to a 5-sigma discovery. The shaded sensitivity region in Figure 7 and the abstract's "probe" language should be reframed as exclusion sensitivity unless the authors define a discovery criterion with a specified significance and account for the uncertainty on the zero-background assumption. This is load-bearing because the central quantitative claim (BR below 1e-4) is derived from a point with about 3.3 selected events.
[Section 4.3 and Section 6] The full sensitivity estimate relies on the displaced-vertex reconstruction efficiency computed with the parametrized Delphes simulation. The custom LCFIPlus configuration (|d0|>2 mm seed tracks, N_trk>=3, m_ch>2 GeV, vertices up to r=2 m) is not validated against a Geant4-based simulation of the IDEA detector, and this is particularly relevant for decays occurring inside the drift-chamber volume at r>34 cm, where track seeding and vertex fitting depend on pattern recognition and material effects that Delphes models only parametrically. The reported reach is linearly proportional to this efficiency: for the (50 GeV, 3e-7) sample, a factor-of-two reduction in signal efficiency would lower the rescaled yield from 3.3 to about 1.6 events, dropping below the three-event threshold. I request that the authors either validate the vertexing efficiency with a full simulation, or provide a systematic uncertainty on the efficiency and quote the resulting uncertainty on the BR reach, or explicitly state that the quoted reach is contingent on the unvalidated Delphes vertexing performance.
[Section 5, Table 3] The conclusion that the selection is background-free is based on zero events surviving from approximately 2.54 million pre-selected background events. With zero observed events, the 95% confidence-level upper limit on the background yield is about three events divided by the number of pre-selected events, i.e., roughly 1.2e-6 per pre-selected event if one treats the pre-selection count as fixed. This statistical bound should be reported explicitly, and it should be propagated into the sensitivity statement, because the "discovery possible" claim assumes exactly zero background. The paper's note that larger MC statistics would be beneficial is appropriate, but it does not quantify the impact on the projected reach.

minor comments (3)

[Section 5] The sentence "The study would therefore benefit from larger MC statistics" would be more useful if accompanied by a quantitative target, such as the number of background events needed to place a given upper limit on the background expectation.
[References] References [10] and [31] appear to share the same DOI (10.17181/nfs96-89q08); please verify that [31] points to the intended vertex-fitting package documentation.
[Figure 2] The y-axis label in Figure 2 appears truncated or malformed ("10^5 10"); please ensure the axis labels and exponents render correctly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the BR~1e-4 projection follows from independent Monte Carlo simulation and an analytic branching-ratio rescaling, not from a fit or self-citation chain.

full rationale

The paper's derivation chain is self-contained and non-circular. Signal samples are generated with an external model (HAHM) and external generators; the dark-scalar lifetime and BR(h to ss) are computed analytically from the Lagrangian parameters via eqs. (2.2)-(2.5), and the selected-event counts follow from independent Delphes/LCFIPlus reconstruction plus the selection in Table 2. The claim that BR around 1e-4 can be probed is obtained in Section 6 by rescaling the Monte Carlo count for the kappa=0.0007 grid point to kappa=0.0002 with 3.3 selected events. This is a scaling of an independent input branching ratio, not a parameter fitted to the result. There are no load-bearing self-citations by the present authors: the cited model, generator, and reconstruction tools (refs. [1,14,15,16,21,32]) are external, and no uniqueness theorem is imported. The explicit caveat in Section 5, that the zero background count carries Monte Carlo statistical uncertainty and the study 'would benefit from larger MC statistics', is a validation caveat rather than evidence of circularity. The main limitation, the absence of a full Geant4 validation of the parametrized displaced-vertex efficiency, affects systematic accuracy but does not reduce the prediction to its inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

No new particles or forces are introduced by this paper. The dark scalar signal is taken from the existing HAHM model. The analysis depends on hand-chosen selection cuts and the assumed validity of the detector simulation.

free parameters (4)

Track transverse impact parameter cut (|d0| > 2 mm) = 2 mm
Chosen to suppress displaced vertices from heavy-flavor decays; directly affects signal acceptance for short-lived scalars and background rejection.
Displaced vertex track multiplicity cut (N_trk >= 3) = 3
Chosen to reject low-multiplicity background vertices while retaining signal vertices from b decays.
Displaced vertex charged invariant mass cut (m_ch > 2 GeV) = 2 GeV
Chosen to reject low-mass background vertices; signal vertices from bbbb final states are expected to have higher mass.
Discovery threshold (selected events) = 3
Arbitrary threshold used to define sensitivity; does not correspond to a 5 sigma significance in a zero-background counting experiment.

assumptions (4)

domain assumption The Hidden Abelian Higgs Model with the dark photon decoupled describes the signal process (Section 2).
The model is taken from prior literature (Curtin et al.) and is not independently validated in this paper.
domain assumption The dark scalar decay width equals sin^2(theta) times the SM Higgs width at the scalar mass (eq. 2.2).
This relation is used to compute lifetimes and is standard for scalar portal models.
domain assumption The branching fraction BR(s -> b bbar) is 0.9 for masses above 10 GeV.
Used to normalize signal yields; taken from prior literature.
domain assumption The Delphes parametrized simulation of the IDEA detector accurately reproduces track, vertex, and lepton reconstruction performance.
The entire analysis relies on this assumption, particularly the displaced vertex efficiency.

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Cite this review

Pith. "Pith review of Searching for long-lived dark scalars at the FCC-ee." pith.science (2026). https://pith.science/paper/BN6UX4XP

@misc{pith2026241210141,
  author       = {Pith},
  title        = {Pith review of: Searching for long-lived dark scalars at the FCC-ee},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BN6UX4XP}},
  note         = {Machine review of arXiv:2412.10141}
}

abstract

This paper investigates the search for long-lived dark scalars from exotic Higgs boson decays at the Future Circular Collider in its $e^+e^-$ stage, FCC-ee, considering an integrated luminosity of 10.8 $\text{ab}^{-1}$ collected during the ZH run at a center-of-mass energy $\sqrt{s}=240$ GeV. The work considers $Zh$ events where the $Z$ boson decays leptonically and the Higgs boson $h$ decays into two long-lived dark scalars $s$ which further decay into bottom anti-bottom quark pairs. The analysis is performed using a parametrized simulation of the IDEA detector concept and targets dark scalar decays in the tracking volume, resulting in multiple displaced vertices in the final state. The sensitivity towards long-lived dark scalars at FCC-ee is estimated using an event selection requiring two opposite-charge, same-flavor leptons compatible with the $Z$ boson, and at least two displaced vertices in the final state. The selection is seen to efficiently remove the Standard Model background, while retaining sensitivity for dark scalar masses between $m_s=20$ GeV and $m_s=60$ GeV and mean proper lifetimes $c\tau$ between approximately 10 mm and 10 m The results show that the search strategy has potential to probe Higgs to dark scalar branching ratios as low as $10^{-4}$ for a mean proper lifetime $c\tau\approx 1$ m. The results provide the first sensitivity estimate for exotic Higgs decays at FCC-ee with the IDEA detector concept, using the common FCC framework.

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Forward citations

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An FCC-ee search for e+e−→Z+invisible scalar could reach σ×BR sensitivities of ~10^-2–10^-1 fb below the Z mass and claims discovery reach up to 80 GeV in a simplified singlet+DM model.

Reference graph

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Curtin et al., Exotic decays of the 125 GeV Higgs boson , Phys

D. Curtin et al., Exotic decays of the 125 GeV Higgs boson , Phys. Rev. D 90 (2014) 075004 [1312.4992]

arXiv 2014

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arXiv

[3] [3]

Liu, L.-T

Z. Liu, L.-T. Wang and H. Zhang, Exotic decays of the 125 GeV Higgs boson at future e+e− lepton colliders , Chin. Phys. C 41 (2017) 063102 [ 1612.09284]

arXiv 2017

[4] [4]

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2019

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S. Alipour-Fard, N. Craig, M. Jiang and S. Koren, Long Live the Higgs Factory: Higgs Decays to Long-Lived Particles at Future Lepton Colliders , Chin. Phys. C 43 (2019) 053101 [1812.05588]

arXiv 2019

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T. Cohen, N. Craig, H.K. Lou and D. Pinner, Folded Supersymmetry with a Twist , JHEP 03 (2016) 196 [ 1508.05396]

work page Pith review arXiv 2016

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G. Burdman, Z. Chacko, H.-S. Goh and R. Harnik, Folded supersymmetry and the LEP paradox, JHEP 02 (2007) 009 [ hep-ph/0609152]. – 12 –

arXiv 2007