Light scalar production from Higgs bosons and FASER 2

Alexey Boyarsky; Anastasia Sokolenko; Iryna Boiarska; Kyrylo Bondarenko; Maksym Ovchynnikov; Oleg Ruchayskiy

REVIEW 3 major objections 6 minor 2 cited by

Light scalar production from Higgs bosons and FASER 2

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read If the invisible Higgs decay rate is at the 5 percent level, FASER 2 can discover the dark scalars produced in h -> SS decays, and a modest doubling of its geometric acceptance extends that reach down to a few GeV in scalar mass.

desk verdict Clear, honest conditional sensitivity study of h->SS at FASER 2; the wide low-mass reach rests on ideal detector assumptions that need a real efficiency/background estimate before being sold as a design driver. read the letter →

arxiv 1908.04635 v2 pith:O56WD3S6 submitted 2019-08-13 hep-ph hep-ex

Iryna Boiarska , Kyrylo Bondarenko , Alexey Boyarsky , Maksym Ovchynnikov , Oleg Ruchayskiy , Anastasia Sokolenko This is my paper · ORCID

classification hep-phhep-ex

keywords Higgsportaldarkscalarlong-livedparticlesFASER2invisibledecayforwardphysicsintensityfrontierhtoSS

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 argues that the quartic Higgs-portal coupling can be large enough that a few to ten percent of LHC Higgs bosons decay invisibly to a pair of new singlet scalars, h -> SS, and that the forward detector FASER 2 is well placed to catch the scalars that decay hundreds of meters downstream. With the fiducial branching ratio BR(h -> SS) = 0.05, the planned FASER 2 geometry should discover scalars with masses between about 40 GeV and m_h/2, and a modest doubling of geometric acceptance — enlarging the decay-vessel radius from 1 m to 1.5 m — extends the reach down to a few GeV. This is possible because the cubic and quartic portal couplings are treated as independent, so the production rate is set by a coupling that invisible-Higgs-decay limits only weakly constrain, while the scalar's decay is controlled by a separate small mixing angle. The result matters because it turns a poorly constrained part of the Higgs portal into a concrete, near-term search target for a proposed LHC forward experiment.

What carries the argument

The load-bearing object is the effective triple-Higgs interaction (α/2) $S^{2}$ h, produced after electroweak symmetry breaking by independent cubic and quartic portal terms in the Lagrangian (1.1). It allows Higgs bosons to decay to a pair of scalars at a rate set by the quartic coupling while the scalar's subsequent decay is set by the separate mixing angle θ; the paper combines this with the forward boost of high-energy Higgs bosons, a geometric-acceptance integral over the scalar angular distribution, and the decay probability P_decay = $e^{{-L/l_decay}}$ - $e^{{-(L+l_det)/l_decay}}$ to predict event rates in the FASER 2 decay vessel.

What would settle it

If the HL-LHC measures the invisible Higgs branching ratio to be below about 5% (or attributes it to channels other than h -> SS), the fiducial event count drops below 2.3 and the quoted mass ranges no longer hold; equivalently, a run of FASER 2 with R = 1.5 m that finds zero displaced scalar decays while BR(h -> SS) is measured at 5% would refute the sensitivity prediction.

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Extended reading notes

Core claim

The central claim is that the process h -> SS, driven by the quartic portal coupling, can dominate all other scalar production channels at the LHC while the scalar's decay remains controlled by the tiny Higgs-mixing angle, and this decoupling makes the FASER 2 event rate factorize into a geometric acceptance times a decay probability. For a fiducial invisible branching ratio of 5%, the paper computes that FASER 2 in its baseline configuration expects at least 2.3 events only for scalar masses in the upper part of the allowed range, approximately 40 GeV ≲ m_S ≲ m_h/2, while increasing the detector radius from 1 m to 1.5 m opens the full range from a few GeV up to m_h/2, with the upper end set by the kinematic threshold and the lower end by geometry. The analytic estimates are checked against Monte Carlo simulations of Higgs production, and the sensitivity curves assume a background-free experiment with 100% detection efficiency.

Load-bearing premise

The load-bearing premise is that the invisible Higgs-decay rate is at least 5 percent and comes entirely from h -> SS; if the true rate is smaller or shared with other channels, all quoted event numbers and mass reach drop proportionally.

Editorial extensions

If this is right

At BR(h -> SS) = 0.05 and with the baseline 1 m radius, FASER 2 will have no sensitivity below roughly 40 GeV, so a null result there would not constrain the model.
Enlarging the FASER 2 radius to 1.5 m extends the sensitivity to every scalar mass from a few GeV up to m_h/2, including the region where existing prompt-decay searches are blind because the scalars have cτ_S ~ O(100) m.
The maximal scalar mass that can be probed is set by the kinematic threshold m_S < m_h/2, not by the usual lifetime-vs-production trade-off, because the production and decay couplings are independent.
Moving the detector closer to the interaction point increases the event rate roughly as L^3, making detector placement a powerful design lever for the scalar portal.
Even if HL-LHC does not discover the invisible Higgs decay directly, FASER 2 can still discover the scalars through their displaced decays, since the signal is not missing energy but reconstructed decay products.

Reading between the lines

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

If the actual invisible branching ratio is closer to the current upper bound of 19% than to the fiducial 5%, the predicted FASER 2 event count scales up by roughly a factor of four, which would extend the reach to smaller values of θ^2 than shown in the paper's sensitivity plot.
The same production/decay decoupling should also change the expected sensitivity of other planned long-lived-particle detectors, whose published reach is usually computed with the production and decay couplings tied together; re-running those analyses with h -> SS as the dominant channel is a natural next step.
A detector-simulation study that replaces the 100% reconstruction-efficiency assumption with realistic tracking and vertexing efficiencies, and that estimates backgrounds near the beam line, would turn the paper's sensitivity contours into firm discovery projections; the paper explicitly leaves that verification to future work.
The same forward-boost and geometric-acceptance machinery could be applied to B-meson production of scalars to quantify the reach below a few GeV, a region the paper identifies but does not compute.

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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

The paper does one clean thing: it takes the general scalar portal with independent cubic and quartic couplings, so h->SS production is set by alpha and decay by theta, and works out what FASER 2 can see. The analytic estimates are transparent, the MadGraph checks are honest, and the main figures are easy to read. The production-decay decoupling is real, and the geometric-acceptance calculation, which is the core of the paper, is done carefully. It is a legitimate, modest contribution to the forward-search program.

The soft spots are the ones the authors themselves flag. The fiducial BR(h->SS)=0.05 is an assumption, not a result: if the invisible width is not dominated by h->SS, or if HL-LHC does not reach 5%, the reach shrinks proportionally. The abstract's "about 10%" is also not derived anywhere; the current 95% bound is 19%, so 10% looks like a conservative round number, not a computed ceiling. More important, the "all masses down to a few GeV" claim for R=1.5 m depends on 100% detection efficiency, 100% visible BR, and zero background. The stress-test note is right: with their own numbers the low-mass event count is O(1), so the dashed contour is a sliver in theta^2; a reconstruction efficiency of 80% or a single background event removes it. The 40-60 GeV region is sturdier and carries the paper's fallback conclusion. So the design recommendation to move from R=1 m to 1.5 m is reasonable, but it should be presented as "under ideal conditions," not as a robust projection.

Minor: the conclusion cites [73] for BR_inv < 0.19, but [73] is a CMS heavy-neutral-lepton search; the correct references are [34,35]. The authors also cite their own Ref. [33] and the earlier FASER dark-Higgs paper [56], so the novelty claim is honest.

Who is this for? People doing forward LLPs and scalar-portal phenomenology. It deserves a serious referee: the physics is sound as a conditional study, and the ideal-detector caveat is a reason to ask for a detector-level follow-up, not a reason to reject. I'd accept it, and I'd push the authors to add a realistic efficiency and background estimate before the radius-increase advice is taken by FASER's collaboration.

Referee Report

3 major / 6 minor

Summary. The paper studies the sensitivity of the FASER and FASER 2 experiments to a light singlet scalar produced through the Higgs portal. In the model of Eq. (1.1), the cubic coupling α₁ and the quartic coupling α₂ are treated as independent, so the production process h→SS (controlled by α₂) and the decay of S to Standard Model particles (controlled by the mixing angle θ) can be decoupled. The authors derive analytic estimates for the number of scalar decays in the FASER decay vessel, cross-check them against MadGraph simulations, and present sensitivity contours in the (m_S, θ²) plane. With a fiducial branching ratio BR(h→SS)=0.05 and the baseline FASER 2 configuration (R=1 m), they find sensitivity only near m_S≈40–60 GeV; increasing the detector radius to 1.5 m is claimed to extend the reach down to a few GeV. The analysis assumes 100% detection efficiency, 100% visible branching, and a background-free experiment, all of which are explicitly flagged by the authors.

Significance. If the central claim holds, the paper provides a concrete, quantitative argument for a modest modification of the FASER 2 geometry (R: 1 m → 1.5 m) that would turn the experiment from a marginal probe of this Higgs-portal scenario into a broad-coverage discovery machine. The analytic framework in Section 2 and the appendices is transparent and largely reproducible, and the cross-check against MadGraph adds credibility to the kinematic treatment. The authors are also explicit about their optimistic assumptions (ε_det=1, BR_visible=1, zero background), which is rare and helpful. The paper's main value is a design-oriented sensitivity projection, not a new theoretical constraint; its conclusions are conditional on BR(h→SS)=0.05 and on the ideal-detector assumptions.

major comments (3)

[§2.1, Eq. (2.15), Eq. (B.14)] The treatment of the h→SS multiplicity is internally inconsistent. Eq. (2.1) defines N_S = 2 N_h BR(h→SS), but Eq. (2.15) computes N_events^(max) = N_h BR_fid ε_geom ⟨P_decay⟩ with no factor of 2, and Eq. (B.14) writes N_det = N_S BR(h→SS) ∫ f P_decay, which double-counts the branching ratio if N_S already contains it. The numerical estimate in §2.1 (N_naive_S ≈ 33) also does not match N_h = 1.7×10^8 and BR_fid = 0.05, which would give ≈19; it corresponds instead to BR ≈ 0.1. Since the sensitivity threshold is 2.3 events, this factor-of-two ambiguity shifts the quoted mass reach and must be resolved. Please state explicitly whether N_h or N_S enters each formula and correct Eq. (2.15) and Eq. (B.14) accordingly.
[§3, Fig. 8, Eq. (2.15)] The low-mass reach of the R=1.5 m configuration rests on O(1) events. Using the paper's own numbers (N_h = 1.7×10^8, BR = 0.05, ε_geom ≈ 4×10^-5 for m_S ≲ 30 GeV, ⟨P_decay⟩ ≈ 3.2×10^-3), the maximum event count is ≈1 (or ≈2 with the factor of two from the previous comment). The dashed contour in Fig. 8 for the R=1.5 m geometry is therefore a narrow sliver in θ², and it disappears entirely if the detection efficiency is below about 80% or if a single background event is present. Because the abstract and conclusion present the "all masses from m_h/2 down to a few GeV" result without this caveat, please add an explicit robustness statement and, if possible, show curves for ε_det < 1 and for a background of one event.
[§1.1, §2.1, Conclusions] All quoted sensitivity scales linearly with BR(h→SS), yet the paper moves among the current bound (BR_inv < 0.19), the HL-LHC projection (0.05–0.15), and the adopted fiducial value 0.05. The abstract's statement that "about 10% of all Higgs bosons" can be converted to scalars may be misread as the value used in the sensitivity analysis, which is actually 5%. Please state explicitly in the abstract and in the caption of Fig. 8 that all mass ranges correspond to BR(h→SS)=0.05 and give the trivial rescaling rule (N_det ∝ BR) so that the reader can evaluate other benchmarks.

minor comments (6)

[§1, p.1] There is a typo: "trough such operators" should be "through such operators".
[Title page] The affiliation of the Leiden authors contains a typo: "Intituut-Lorentz" should be "Instituut-Lorentz".
[§2.3] The sentence "all major decay channels have > 2 charged tracks" should be "≥ 2 charged tracks", since the dimuon final state has exactly two charged tracks.
[Conclusions, Ref. [73]] The bound BR_inv < 0.19 is cited to Ref. [73], which is a CMS search for heavy neutral leptons; the correct reference for the invisible Higgs decay constraint is Ref. [34] (CMS, Phys. Lett. B793 (2019) 520).
[Table 1] The same symbol L is used for integrated luminosity and for the distance to the detector, which is confusing; please use e.g. ℒ for luminosity and d (or L_dec) for the distance.
[§3, Fig. 8 caption] The caption says the sensitivity estimates assume 100% reconstruction efficiency, but the main text also assumes zero background and 100% visible branching. These two additional assumptions should be stated in the caption as well, since the figure is the basis of the paper's headline claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the sensitivity curves follow from an externally supplied fiducial branching ratio, standard kinematic acceptances, and a Poisson event-count threshold, not from a fitted or self-referential quantity.

full rationale

The derivation is self-contained and conditional rather than circular. The number of events is computed as N_det = N_S * epsilon_geom * P_decay * epsilon_det (Eq. 2.1), where N_S = 2 N_h BR(h -> S S) uses the externally adopted fiducial value BR_fid(h -> S S) = 0.05 from projected HL-LHC sensitivity (Eq. 2.3), not a value fitted to FASER data. The geometric acceptance epsilon_geom is obtained from simulated Higgs boson momentum distributions via Eqs. (2.8)-(2.10), and the decay probability P_decay from the standard formula (2.2) with lifetimes controlled by the mixing angle theta. The sensitivity region in Fig. 8 is then simply the set of (m_S, theta^2) giving at least 2.3 events under the explicitly stated background-free, unit-efficiency assumptions. No predicted quantity is equivalent by construction to an input parameter: the production coupling alpha is fixed by the assumed branching ratio, while the decay coupling theta is scanned to produce the sensitivity contour. The self-citations, notably Ref. [10] for scalar decay widths and Ref. [51] for the event-count formula, supply standard, parameter-free inputs (QCD decay rates and the well-known N_det formula) whose assumptions do not include the FASER sensitivity result; they are therefore independent support rather than a circular chain. The paper also explicitly labels its optimistic assumptions ('we optimistically assume detector efficiency eps_det = 1', 'we assume background free experiment'), which are limitations on robustness, not circularity. Accordingly, no step satisfies the requirement of being reducible to its own input by definition or by a fitted parameter renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central sensitivity projection depends on a fiducial Higgs to scalar branching ratio, two ideal detector assumptions, and several physics inputs taken from prior literature, including the authors' own calculations. No new particles or forces are introduced beyond the standard singlet scalar of the Higgs portal model.

free parameters (3)

Fiducial branching ratio BR(h to SS) = 0.05
Chosen as a benchmark equal to the lower bound of projected HL-LHC invisible Higgs sensitivity (Ref [62]); the predicted event rate is directly proportional to this number.
Detection efficiency epsilon_det = 1
Assumed 100 percent efficiency for reconstructing scalar decays, explicitly described as optimistic by the authors in Sections 2.1 and 3.
Visible branching ratio BR(S to visible) = 100 percent
Assumed every decay has at least two charged tracks and is reconstructable; authors note verification requires detector studies beyond the paper's scope (Section 2.3).

assumptions (5)

domain assumption The Higgs production cross-section at HL-LHC is about 55 pb at 13 TeV, giving Nh = 1.7e8 produced Higgs bosons.
Used to set the normalization of produced scalars; taken from the HL/HE WG report [70].
domain assumption The momentum distributions of Higgs bosons from MadGraph5 aMC@NLO, following [72], correctly describe forward production.
All acceptance and energy estimates use these distributions; validated against [72] and [75] in Appendix A with up to 30 percent difference in the forward fraction.
domain assumption Scalar decay widths and branching ratios from the perturbative QCD calculations of Ref [10] are accurate.
Decay length and visible branching fractions are taken from this self-cited previous paper; no independent reproduction is provided.
ad hoc to paper FASER and FASER 2 are background-free experiments.
Sensitivity is defined as 2.3 events with zero background; the paper acknowledges this assumption but does not justify it with detector background studies (Section 3).
domain assumption Scalar production via off-shell Higgs or B-meson decays is negligible for mS above about 5 GeV.
The analysis restricts to mS > 5 GeV and ignores those channels, citing prior work [10]; this limits the lowest masses covered.

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Cite this review

Pith. "Pith review of Light scalar production from Higgs bosons and FASER 2." pith.science (2026). https://pith.science/paper/O56WD3S6

@misc{pith2026190804635,
  author       = {Pith},
  title        = {Pith review of: Light scalar production from Higgs bosons and FASER 2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O56WD3S6}},
  note         = {Machine review of arXiv:1908.04635}
}

abstract

The most general renormalizable interaction between the Higgs sector and a new gauge-singlet scalar $S$ is governed by two interaction terms: cubic and quartic. The quartic interaction is only loosely constrained by invisible Higgs decays. Given current experimental limits about $10\%$ of all Higgs bosons created at the LHC can be converted to new scalars with the mass up to $m_{\rm Higgs}/2$. This can significantly extend the reach of the LHC-based Intensity Frontier experiments. We analyze the sensitivity of the FASER experiment to this model and discuss modest changes in the FASER 2 design that would allow to explore an orders-of-magnitude wider part of the Higgs portal's parameter space.

Discussion (0). Continue with ORCID to comment.

Forward citations

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