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Heavy Neutral Leptons without Prejudice

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Treating the HNL Yukawa coupling and the active-sterile mixing angle as independent parameters, this paper maps where the HL-LHC and FCC-ee can discover or exclude heavy neutral leptons, and finds that when there is no mixing, the…

desk verdict Useful FCC-ee extension of an HNL study; the qualitative conclusions hold, but the central HL-LHC vs FCC-ee comparison needs a common analysis protocol before it is quantitative. read the letter →

arxiv 2412.12271 v2 pith:VJQEZ4VC submitted 2024-12-16 hep-ph hep-ex

Nicolás Bernal , Kuldeep Deka , Marta Losada This is my paper · ORCID
classification hep-phhep-ex
keywords heavyneutralleptonsactive-sterilemixingYukawacouplingHiggswidthdisplacedverticeslong-livedparticlesFCC-eeHL-LHC
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

Heavy neutral leptons are a leading extension of the Standard Model because they can explain neutrino masses, leptogenesis, and dark matter, but their collider signatures depend on two couplings that many models tie together. This paper deliberately drops that tie: it treats the Yukawa coupling $y$ (to the Higgs boson) and the active-sterile mixing angle $V$ (to the $W$ and $Z$ bosons) as independent free parameters, and asks which measurements would actually find HNLs in each corner of the resulting parameter space. The study computes production and decay rates for HNLs of masses between 2 and 120 GeV and derives $3\sigma$ discovery or 95% exclusion contours for the HL-LHC (prompt, displaced, and FASER-2 far-detector searches) and for FCC-ee (Z-pole and $Zh$ modes). The central finding is that for $V=0$ the sensitivity to $y$ is set by the Higgs width measurement at both colliders, while for $V\neq 0$ the mixing angle dominates and severely shrinks the allowed parameter space. If correct, the reach contours in the paper tell experimentalists which search channel is worth building and which precision measurement closes the remaining window.

What carries the argument

The carrying object is the $(y^2, V^2)$ plane at fixed HNL mass $m_N$, divided into prompt, displaced ($1$ mm $\le d_{xy} \le 1$ m, $d_z \le 300$ mm), and long-lived ($c\tau \sim 480$ m) regimes by lifetime contours. The carrying identities are the partial widths: $\Gamma(h\to N\nu) = \frac{y^2}{8\pi} m_h \left(1 - m_N^2/m_h^2\right)^2$ for Yukawa production, and the gauge-mediated widths $\Gamma(W^\pm \to N\ell^\pm_\alpha)$ and $\Gamma(Z\to N\nu)$ proportional to $V^2$. These widths determine both the signal rates at each collider and the Higgs total and invisible width bounds that produce the vertical exclusion bands on $y^2$. The analysis chains these widths through VBF single-Higgs production at the HL-LHC, through $Z$-pole and $Zh$ production at FCC-ee, and through the FASER-2 acceptance geometry for long-lived decays.

What would settle it

Run the identical VBF and displaced-vertex selections with a full detector simulation at high pileup, measure the b-tagging, lepton-veto, and displaced-track reconstruction efficiencies, and count background events in the full HL-LHC dataset instead of scaling the 139 fb$^{-1}$ ATLAS number; if the product of efficiencies falls noticeably below unity or the background exceeds roughly 65 events, the contours in Figs. 3, 6, and 9 move away from the low-$y$, low-$V$ corner and the stated HL-LHC and FCC-ee complementarity in that corner no longer holds.

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Extended reading notes

Core claim

The paper's central claim is that a model-independent, two-coupling treatment of HNLs changes the search strategy. By keeping $y^2$ and $V^2$ independent, it finds that the type-I seesaw relation $V = y v_h/m_N$ is not a reliable guide: Yukawa-dominated HNLs exist in models such as inverse seesaw, and for them the strongest constraint is not a dedicated search but the precision measurement of the Higgs boson width. In the zero-mixing case, the HL-LHC and FCC-ee reaches on $y$ are comparable, and Higgs width measurements impose the strongest constraints; in scenarios with nonzero mixing, sensitivity is dominated by the active-sterile mixing angle, with FCC-ee providing stringent limits. The paper also shows that FASER-2 can reach long-lived HNLs with $c\tau \sim 480$ m, and that displaced-vertex searches inside ATLAS and CMS cover the intermediate lifetime region. The overall implication is that HNL parameter space is best probed by a combination of precision Higgs physics and displaced or long-lived searches rather than prompt-only searches.

Load-bearing premise

The load-bearing premise is that the detector response is ideal, meaning 100% b-tagging, lepton-veto, and displaced-track reconstruction efficiency, with backgrounds either zero or a fixed 65 events at 3 ab$^{-1}$ obtained by linearly scaling ATLAS's 139 fb$^{-1}$ count; if real efficiencies are lower or backgrounds scale nonlinearly, the $3\sigma$ contours in the low-$y$, low-$V$ region shift and the claimed complementarity weakens.

Editorial extensions

If this is right

  • If HNLs with $V=0$ exist, the HL-LHC and FCC-ee will not beat each other on $y$; instead, improving the Higgs width measurement to the projected 5.3% (HL-LHC) and 1% (FCC-ee) precision is the surest route to exclude or discover them.
  • For nonzero mixing, resources are best spent on mixing-sensitive searches such as gauge-boson production and displaced vertices, because $V$ controls both production and decay in that region.
  • FASER-2 extends the HL-LHC program to HNLs with lifetimes around 480 m, covering masses down to 2 GeV that prompt and inner-tracker searches do not reach.
  • At FCC-ee, the Z-pole phase with 204 ab$^{-1}$ can exclude significant mixing parameter space for HNL masses near 10 to 20 GeV, while the $Zh$ phase mainly probes the Yukawa-only corner.
  • The free-parameter treatment makes the exclusion contours portable: any model that fixes the relation between $y$ and $V$ can be checked against these figures without redoing the collider simulation.

Reading between the lines

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

  • Beyond the paper: the most cost-efficient near-term probe of Yukawa-dominated HNLs is the Higgs width and invisible-width program, because those measurements scan all HNL masses below $m_h/2$ at once without requiring new detectors.
  • Beyond the paper: the same decouple-the-couplings logic should apply to any Higgs-portal hidden fermion, so the conclusion that precision width beats dedicated searches in the zero-mixing limit likely generalizes to other new-physics scenarios with suppressed mixing.
  • Beyond the paper: if an HNL signal is ever observed, its location in the $(y^2,V^2)$ plane would discriminate seesaw mechanisms: points far above the type-I seesaw line imply suppressed mixing such as inverse seesaw, while points near the line are consistent with canonical type-I seesaw.
  • Beyond the paper: the appendix's recast shows that existing mixing limits do not translate into useful Yukawa limits except in regions already excluded by Higgs-width constraints, implying that new Higgs-precision and displaced searches are the only realistic way to test Yukawa-dominated HNLs.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper presents a model-independent collider study of heavy neutral leptons (HNLs) in which the active-sterile mixing parameter V^2 and the Higgs Yukawa coupling y^2 are treated as independent free parameters. The authors compute HNL production and three-body decay widths with MadGraph (HeavyN model), then project sensitivities at the HL-LHC for prompt VBF Higgs decays h -> N nu (N -> nu b bbar), displaced vertices in the inner tracker, and long-lived decays into FASER-2. For FCC-ee they study the Z-pole and Zh (240 GeV) stages in both prompt and displaced channels, including a zero-mixing scenario and scenarios with nonzero mixing. The main conclusions are that (i) for zero mixing the HL-LHC and FCC-ee have comparable sensitivity to y^2, with the Higgs total and invisible width measurements providing the strongest constraints; and (ii) for nonzero mixing, the sensitivity is dominated by V^2, with the FCC-ee Z-pole providing stringent limits. The appendix recasts existing mixing limits from the (V^2, m_N) plane onto the (V^2, y^2) plane and finds no additional constraining power.

Significance. Decoupling y^2 from V^2 is a useful and increasingly relevant way to present HNL searches, since specific models (inverse seesaw, radiative models) violate the naive type-I seesaw relation; the reach curves in Figs. 2-9 map where each coupling dominates and where neither collider helps. Credit is due for concrete elements: explicit cut lists (S1-S7), standard widths and cross sections, externally referenced constraints (Higgs width, invisible width, mixing limits), public tool usage (MadGraph, FeynRules/HeavyN), and an appendix that honestly recasts existing limits (finding no additional power). The paper is also candid that the zero-background displaced assumption 'might be overly optimistic' (Sec. 4.2) and that the mu-jj channel with better reach is not considered (Sec. 5.1 footnote). The scientific value is moderate: these are projections without full detector simulation, but that is normal for this literature. The result would be significant if, after a matched-protocol comparison, the zero-mixing comparability claim survives.

major comments (3)
  1. [Sec. 6; Fig. 7 (left); Secs. 4.1, 5.1.2, 5.2.3] The central zero-mixing claim of Section 6 ('no significant enhancement in sensitivity to the Yukawa coupling when comparing the HL-LHC and FCC-ee') is a relative statement, but the two arms of Fig. 7 (left) are not computed under a common protocol. The HL-LHC prompt contours of Sec. 4.1 are 3-sigma discovery reaches for which no post-cut background yields, signal efficiencies, or significance formula are reported; the HL-LHC displaced contours are imported from Ref. [120] without restating their assumptions; and the FCC-ee displaced contours of Secs. 5.1.2 and 5.2.3 are drawn for 1, 10, and 100 observed events with no background or efficiency model stated. The caption of Fig. 7 does not say whether the blue FCC-ee contour is prompt, displaced, or combined, nor at which confidence level or event count. Because the two searches use different production modes (VBF Higgs at 14 TeV versus Zh at 240 GeV) and different counting definitions, mismatched confidence levels or efficiency assumptions can move the curves relative to each other by a large factor in y^2. The comparison should be re-run under a matched protocol (same significance definition, same background treatment, same efficiency assumptions applied to both colliders), or the authors should provide a table of the y^2 reach at fixed m_N under identical assumptions; as written, the paper establishes comparability only under two different, only partially documented analysis recipes.
  2. [Sec. 4.2; Fig. 3] The pessimistic displaced-vertex contour in Sec. 4.2 is obtained by taking a maximum of 3 background events from the ATLAS 139 fb^-1 analyses of Refs. [148, 149] and scaling them linearly to 65 events at 3 ab^-1. Linear scaling assumes the background is produced by processes whose rate is proportional to integrated luminosity and that no background-rejection improvement applies to the VBF-based selection (cuts S1, S3, S4 plus the displaced-jet requirements), which differs from the ATLAS selections being scaled. The factor of 65 directly shifts the thin contours in Fig. 3 and hence the size of the robustly excluded region. Please either justify the linear scaling for the present selection or treat the background parametrically (for example, show contours for 0, 3, and 65 background events, or for a sqrt(L) or saturating scaling) so the reader can see which parts of the exclusion region do not depend on this assumption.
  3. [Secs. 4.1, 4.2, 5.1.2, 5.2.3] The analyses never state the assumed reconstruction and tagging efficiencies. The prompt search applies the lepton/photon veto (S1) and the b-tag requirement (S2) as if they were perfectly efficient, and the displaced searches impose the window '1 mm <= d_xy <= 1 m and d_z <= 300 mm' with no tracking or vertex-finding efficiency. These efficiencies enter multiplicatively in the signal count, so the reach in y^2 scales as 1/epsilon at fixed event count; for epsilon = 0.5 the contours move by a factor of about two in y^2, which is the same order as the apparent separation between the HL-LHC and FCC-ee curves in Fig. 7 (left). The authors should state the efficiency assumptions explicitly and, ideally, quantify the sensitivity of the key contours (Figs. 3, 6, 7, and 9) to them.
minor comments (5)
  1. [Sec. 3] In the width compilation of Sec. 3, the quoted errors are mutually inconsistent within one paragraph: Gamma(Z -> nu nubar) = (501 +/- 0.045) MeV versus Gamma(Z -> inv) = (500 +/- 1.5) MeV, and Gamma(W+/- -> nu l+/-) = 679 +/- 0.12 MeV versus 679 +/- 0.01 MeV. Please harmonize these numbers with the PDG values cited as [131].
  2. [Fig. 5 caption] The caption of Fig. 5 says 'for three benchmark masses of the HNL, namely 45 and 70 GeV,' but the figure contains only two panels; correct the caption or add the m_N = 20 GeV panel used elsewhere.
  3. [Fig. 7 (left); Sec. 5.2.1] Fig. 7 (left) and Sec. 5.2.1 do not specify whether the blue FCC-ee contour is the prompt-only, displaced-only, or combined reach, nor which event-count threshold or confidence level it corresponds to; please state this in the caption (see also Major comment 1).
  4. [Secs. 4.2, 5.1.2, 5.2.3] The displaced-vertex window '1 mm <= d_xy <= 1 m and d_z <= 300 mm' is applied to the FCC-ee searches (Secs. 5.1.2 and 5.2.3) without stating the FCC-ee inner-tracker geometry; the maximum observable d_xy should be tied to the assumed detector radius.
  5. [Sec. 5.2.1; Fig. 7 (right)] The right panel of Fig. 7 introduces 'FCC-ee h pole' runs at 10 ab^-1 and 35 ab^-1, but Sec. 5.2.1 does not explain this operating mode (presumably e+e- -> h at sqrt(s) = m_h) or where these luminosity assumptions come from; please add one sentence of context.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; the central FCC-ee/LHC comparison rests on external constraints and a separate prior HL-LHC analysis ([120]), not on a fitted parameter or a self-referential definition.

full rationale

The paper's projected reaches are computed from model inputs (Yukawa and mixing couplings), analytic partial widths (Sec. 3, Eqs. 3.1-3.3), MadGraph event generation with the HeavyN model, and Poisson event counting for displaced signatures (Secs. 4.2, 4.3, 5.1.2, 5.2.3). No parameter is fitted to data and then presented as a prediction. External inputs--PDG widths, ATLAS/CMS Higgs invisible and total width bounds, DELPHI/LEP and other mixing limits, and ATLAS background inputs from Refs. [148,149]--are used as constraints and calibration anchors, not as outputs of the derivation. The zero-mixing 'comparable sensitivity' claim is a comparison between the new FCC-ee calculation and the HL-LHC contours from the authors' earlier paper [120]. Although this is a self-citation and it is load-bearing for the relative statement, Ref. [120] is a separate published analysis with its own stated cuts and assumptions; it does not presuppose the FCC-ee result, and its contours are externally checkable rather than being recycled as the conclusion. The caveat that the two arms use different thresholds, background treatments, and event-count conventions is a robustness or protocol concern, not a circularity. Appendix A's recast (Eq. A.1) is a projection of existing V^2 limits onto the [V^2, y^2] plane with a branching-ratio correction, and the paper explicitly notes it provides no new insight; this is an honest mapping, not a renamed prediction. The statement that the Higgs width gives the strongest constraint follows from the computed h -> N nu width and the projected width uncertainties, so it is not an input disguised as an output. Overall, the derivation is self-contained apart from the minor, non-circular reliance on the prior HL-LHC study; score 1.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's central results rest on no fitted parameters: y^2 and V^2 are scanned model inputs. The analysis does introduce hand-chosen benchmarks, cut thresholds, and a linear background scaling that affect the contours, and it assumes idealized detector performance. The HNL itself and the SM effective couplings are not invented here; they are prior literature inputs.

free parameters (3)
  • Displaced-background event count at 3 ab^-1 = 65 events
    Chosen by hand in Section 4.2 by scaling ATLAS's 3 observed events at 139 fb^-1 linearly; it directly sets the pessimistic sensitivity contour in Fig. 3 and similar displaced analyses.
  • Benchmark HNL masses = 2, 5, 10, 20, 45, 70 GeV
    Chosen ad hoc for the sensitivity scans; the reach in the (y^2, V^2) plane depends on mN through the decay widths and the kinematic cuts (e.g., m_bb windows).
  • Selection cut thresholds = pT > 60/40 GeV, HT > 140 GeV, Delta_eta > 3.5, m_j1j2 > 500 GeV, etc.
    Chosen by hand and labelled 'optimization' without a formal optimization procedure; they set the signal acceptance and background rejection and therefore the exact position of the 3-sigma contours.
assumptions (4)
  • standard math The production and decay widths in Eqs. (3.1)-(3.3) are complete and correct for the HNL interactions considered.
    Standard results from the HNL literature; the paper cites [120] and PDG values but does not rederive them.
  • domain assumption The Yukawa coupling y and the active-sterile mixing V can be treated as independent free parameters.
    Core of the 'without prejudice' approach; justified by references to inverse-seesaw and zero-mixing models [120,126,127], but the naturalness or generality of this decoupling is not demonstrated.
  • ad hoc to paper Background events for displaced searches scale linearly with luminosity from 139 fb^-1 to 3 ab^-1.
    Section 4.2; used to set the 65-event pessimistic background, with no justification that background composition scales linearly.
  • ad hoc to paper Detector response can be modeled by purely geometric and kinematic cuts with 100% efficiency.
    Sections 4 and 5; no efficiency, resolution, or fake-rate modeling is included, which is an optimistic assumption for the projected reaches.

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Cite this review

Pith. "Pith review of Heavy Neutral Leptons without Prejudice." pith.science (2026). https://pith.science/paper/VJQEZ4VC

@misc{pith2026241212271,
  author       = {Pith},
  title        = {Pith review of: Heavy Neutral Leptons without Prejudice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VJQEZ4VC}},
  note         = {Machine review of arXiv:2412.12271}
}
abstract

Heavy Neutral Leptons (HNLs) provide a compelling extension to the Standard Model, addressing the neutrino masses, baryogenesis, and dark matter problems. We perform a model-independent collider study, decoupling the active-sterile mixing angle ($V$) from the Yukawa coupling ($y$), and explore sensitivities at the HL-LHC for prompt and displaced decays. We also consider the possibility of HNLs being long-lived particles decaying in far detectors as FASER. In addition, we study the expected reach at FCC-ee for the prompt and displaced cases. For zero mixing, FCC-ee and HL-LHC sensitivities to $y$ are comparable, with Higgs width measurements imposing the strongest constraints. With non-zero mixing, sensitivities are dominated by $V$, significantly constraining parameter space. This work highlights the importance of precision Higgs studies and displaced searches in probing HNLs at current and future colliders.

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