{"id":"2fe70b75-5294-4b89-b174-59a8dbfc5082","arxiv_id":"2412.12271","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"HL-LHC and FCC-ee can probe HNL Yukawa couplings down to y^2 near 10^-4 to 10^-6 depending on mass; at zero mixing, Higgs width precision is the strongest constraint and the two colliders have comparable reach.","lead":"The paper maps how future colliders could discover heavy neutral leptons that interact through the Higgs boson, separate from their neutrino-mixing strength. It finds the HL-LHC and FCC-ee have similar reach when mixing is zero, with Higgs width measurements setting the strongest limits, and that mixing dominates once it is included.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"HL-LHC vs FCC-ee 'comparable' claim rests on non-identical analysis thresholds; a common-protocol re-run is needed before the central zero-mixing conclusion is secure.","rationale":"I read the paper in good faith. The model-independent decoupling of y and V is a reasonable and clearly stated framework, and the internal logic of the nonzero-mixing conclusion (V dominates sensitivity) follows from the plotted contours and existing constraints. The Higgs-width argument for the zero-mixing case is also internally consistent, since the total width constraint applies regardless of the HNL decay topology. The soft spot is the comparison protocol underlying the central relative claim. The reader's weakest assumption (idealized detector performance and background scaling) is closely related, but the more precise issue is that the two arms of the comparison are not computed with matched statistical thresholds or a matched detector model. The HL-LHC displaced contours use 3.09 events at 95% CL or a linearly scaled 65-event background, while the FCC-ee displaced contours are simply drawn for 1, 10, and 100 events; the prompt analyses quote discovery-style contours with no background tables. This does not make the paper internally inconsistent, but it does make the headline 'no significant enhancement' underdetermined. The fix is straightforward: rerun both facilities with a common efficiency and event-count convention. Because this concern is testable and does not by itself overturn the work, I keep the reader's conditional verdict unchanged. I also note that the absence of released code or model files, flagged by the reader, compounds the difficulty of checking the comparison, but it is not the load-bearing physics issue.","tokens_in":20326,"tokens_out":16720,"duration_ms":172093,"concrete_test":"Recompute Fig. 7 left for V=0 using one shared analysis protocol: the same event-count threshold (e.g., 95% CL upper limit with a fixed background of 3 events), the same b-tagging efficiency (e.g., 70%), lepton-veto efficiency (90%), and displaced-track efficiency (80%) applied to both HL-LHC VBF and FCC-ee Zh production, using identical HNL production and decay tables. If the two contours remain within a factor of about 2 in y^2 for all m_N, the concern is resolved; if they separate by more than a factor of about 5 at any mass, the headline 'no significant enhancement' should be revised or conditioned on the specific analysis choices.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 6's central zero-mixing claim ('no significant enhancement ... when comparing the HL-LHC and FCC-ee') is supported in Fig. 7 left by overlaying HL-LHC contours taken from Ref. [120] with FCC-ee contours derived here. These two sets are not computed under a common protocol. The LHC prompt search (Sec. 4.1) quotes 3-sigma contours but reports no post-cut background yields, signal efficiencies, or systematic uncertainties; its background list (ggF h->bb, tt+jets, bb+jets) is not converted into a significance formula. The LHC displaced search (Sec. 4.2) uses 3.09 events at 95% CL for the zero-background contour and, for the pessimistic case, 65 events obtained by linearly scaling ATLAS 139/fb data. The FCC-ee displaced contours (Secs. 5.1.2 and 5.2.3) are drawn for 1, 10, and 100 observed events, with no stated background or efficiency model. Because the headline statement is a relative statement, any mismatch in confidence level, background treatment, or assumed b-tag/lepton-veto/vertex efficiency between the two arms can move the curves relative to each other by an order of magnitude in y^2. As written, the comparison therefore does not yet establish that the two facilities have comparable reach; it establishes comparability under two different, undocumented analysis recipes.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20610,"tokens_out":13900,"duration_ms":119109,"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":[{"comment":"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.","section":"Sec. 6; Fig. 7 (left); Secs. 4.1, 5.1.2, 5.2.3"},{"comment":"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.","section":"Sec. 4.2; Fig. 3"},{"comment":"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.","section":"Secs. 4.1, 4.2, 5.1.2, 5.2.3"}],"minor_comments":[{"comment":"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].","section":"Sec. 3"},{"comment":"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.","section":"Fig. 5 caption"},{"comment":"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).","section":"Fig. 7 (left); Sec. 5.2.1"},{"comment":"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.","section":"Secs. 4.2, 5.1.2, 5.2.3"},{"comment":"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.","section":"Sec. 5.2.1; Fig. 7 (right)"}],"recommendation":"major_revision","confidential_remarks":"This is a solid phenomenological projection paper, well within the scope of a hep-ph journal. The main risk is the headline comparative claim (HL-LHC versus FCC-ee for zero mixing), which rests on two non-matched analyses; this is fixable with a common-protocol cross-check and should be required before publication. The detector modeling is idealized, but that is comparable to the field's standard for projection papers; I would not demand full simulation, only explicit efficiency statements and a parametric background treatment. The reference list is appropriate and does not over-cite the authors' own work; Ref. [120] is the natural prior to this paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a competent, useful extension of Bernal, Deka, Losada's earlier LHC-only HNL study. The genuinely new value is the FCC-ee part: Z-pole and Zh searches, the joint (y^2, V^2) reach plots, and the explicit statement that with zero mixing the projected Higgs width measurement is the tightest constraint. That last point is the paper's strongest result, and it holds up.\n\nThe setup is clean: y and V are treated as independent, decay widths are standard, and the selection cuts are spelled out. The appendix recast of existing mixing limits onto the (y^2, V^2) plane is a nice touch and shows they have not ignored competing searches.\n\nThe soft spots are real but not disqualifying. The headline comparison between HL-LHC and FCC-ee for the zero-mixing case overlays contours from Ref. [120] with contours derived here, and the two analyses do not share a common protocol. Different cuts, different background treatments (zero background for some curves, 65 linearly scaled events for others), and possibly different confidence levels are being compared. If efficiencies or backgrounds shift, the relative position of the two reaches could move by an order of magnitude in y^2. The paper does not provide signal efficiencies or post-cut background yields, so a reader cannot correct for this without redoing the analysis. A common-protocol re-run would settle it.\n\nAlso, the displaced-vertex and far-detector projections assume idealized detector performance: 100% tagging and reconstruction efficiency, no systematic uncertainties. The 65-event background number is a rough linear scaling from 139 fb^-1, which is a crude approximation. No code or model files are released, so reproducing the contours means re-implementing the analysis from the text.\n\nNone of this kills the paper's qualitative conclusions. The Higgs-width dominance in the zero-mixing case follows from the projected precision of the width measurement itself, not from the details of the collider analysis. The nonzero-mixing conclusion that V dominates is also robust. But the quantitative reach curves in Figs. 3, 6, 7, and 9 should be treated as indicative, not as final sensitivity numbers.\n\nWho this is for: people working on HNL searches at the HL-LHC and future e+e- colliders, and anyone making the physics case for FCC-ee. It deserves a serious referee and, after revision, publication. I would send it out.","headline":"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.","tokens_in":21154,"tokens_out":2416,"would_cite":true,"duration_ms":22237,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["heavy neutral leptons","active-sterile mixing","Yukawa coupling","Higgs width","displaced vertices","long-lived particles","FCC-ee","HL-LHC"],"falsifier":"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.","tokens_in":20088,"feed_emoji":"⚛️","tokens_out":9674,"duration_ms":83652,"temperature":0.7,"pith_summary":"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.","feed_headline":"With no mixing, Higgs width is the strongest HNL constraint","feed_subtitle":"A model-free study maps where HL-LHC and FCC-ee can still discover heavy neutral leptons.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"It defines the zero-mixing VBF Higgs-production analysis at the HL-LHC and the decoupling of $y$ from $V$ that this paper extends to FCC-ee.","marker":"[120]"},{"why":"It supplies the inclusive displaced-vertex search strategy and the background treatment used for the LHC displaced reach.","marker":"[70]"},{"why":"It provides the most stringent current limits on the active-sterile mixing angle $V^2$ used for the exclusion bands and the appendix recast.","marker":"[134]"},{"why":"It defines the FASER detector geometry and physics case that set the far-detector long-lived HNL reach.","marker":"[96]"},{"why":"It specifies the FASER-2 phase at the HL-LHC, including its size and luminosity, used in the long-lived sensitivity calculation.","marker":"[97]"},{"why":"It gives the FCC-ee operating parameters, including Z-pole and Zh luminosities, that set the FCC-ee reach estimates.","marker":"[119]"},{"why":"It supplies the projected 5.3% HL-LHC precision on the Higgs width used as the leading constraint on $y$ in the zero-mixing case.","marker":"[132]"},{"why":"It supplies the projected 1% FCC-ee precision on the Higgs width used for the corresponding FCC-ee constraint.","marker":"[133]"},{"why":"It provides the ATLAS limit on invisible Higgs decays that sets the vertical exclusion band at low $m_N$.","marker":"[140]"}],"fun_headline_variants":["Higgs width beats direct HNL searches for zero mixing","Zero-mixing HNLs? Higgs width is the strongest probe","Yukawa-driven HNLs: Higgs precision wins over direct detection","FCC-ee and HL-LHC tie on HNLs, Higgs width wins"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Higgs width beats direct HNL searches for zero mixing","Zero-mixing HNLs? Higgs width is the strongest probe","Yukawa-driven HNLs: Higgs precision wins over direct detection","FCC-ee and HL-LHC tie on HNLs, Higgs width wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000558,"raw_usage":{"total_tokens":2644,"prompt_tokens":925,"completion_tokens":1719,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":541,"completion_tokens_details":{"reasoning_tokens":1641}},"tokens_in":541,"tokens_out":1719,"duration_ms":11678,"temperature":1.0,"reasoning_tokens":1641,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:14:59.418425+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}