Heavy neutral leptons and top quarks in effective field theory

Arsenii Titov; Giovanna Cottin; Julian G\"unther; Martin Hirsch; Rebeca Beltr\'an; Zeren Simon Wang

REVIEW 2 major objections 4 minor 1 cited by

Heavy neutral leptons and top quarks in effective field theory

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper claims that displaced-vertex searches at the HL-LHC could probe top-HNL effective couplings up to new-physics scales of about 12 TeV at ATLAS and 4.5 TeV at MATHUSLA and ANUBIS.

desk verdict Solid, genuinely new LLP sensitivity projections for top-philic HNL operators; headline reach rests on an unvalidated zero-background assumption, but the paper's own 10/30-event contours keep it honest. read the letter →

arxiv 2501.09065 v3 pith:NDQTXEN5 submitted 2025-01-15 hep-ph

Rebeca Beltrán , Giovanna Cottin , Julian Günther , Martin Hirsch , Arsenii Titov , Zeren Simon Wang This is my paper · ORCID

classification hep-ph

keywords heavyneutralleptonslong-livedparticlesdisplacedverticeseffectivefieldtheorytopquarkHL-LHCMATHUSLAANUBIS

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 tries to establish that long-lived heavy neutral leptons (HNLs) coupled to top quarks through dimension-six effective operators could be probed or excluded at the high-luminosity LHC using displaced vertices. The authors classify the production and decay of HNLs from four-fermion top-HNL operators, and compute sensitivity projections for ATLAS and the proposed far detectors MATHUSLA, ANUBIS, CODEX-b, and MAPP2. For the pair-production operator $\mathcal{O}^{13}_{uN}$ with coefficient $c/\Lambda^2 = 1\,\mathrm{TeV}^{-2}$, they estimate that ATLAS could probe new-physics scales up to about 12 TeV, while MATHUSLA and ANUBIS reach about 4.5 TeV, over complementary HNL mass ranges. A sympathetic reader would care because these operators escape present top-width constraints, so a displaced-vertex search would turn the HL-LHC into a probe of few-TeV top-philic new physics.

What carries the argument

The load-bearing object is the set of dimension-six four-fermion operators coupling a right-handed heavy neutral lepton $N_R$ to top quarks, each entering with Wilson coefficient $c/\Lambda^2$, together with the displaced-vertex machinery used to count signal events. In the pair-NR operator case, production is controlled by the operator while decay is controlled by the active-sterile mixing $|V_{eN}|^2$; in the single-NR operator case the same operator feeds both production and decay, including loop-induced three-body decays. ATLAS sensitivities are obtained by applying jet and vertex requirements to simulated events and using the ATLAS DV+jets parameterized efficiencies, while far-detector sensitivities come from the probability that a simulated HNL decays inside each detector's fiducial volume, all evaluated at $\sqrt{s}=14$ TeV and $L=3\,\mathrm{ab}^{-1}$.

What would settle it

Simulate a full Standard Model background sample through the proposed ATLAS search chain — the 4/5/6-jet thresholds with $p_T > 90/65/55$ GeV, vertices with $4 < R_{xy} < 300$ mm, $|d_0| > 2$ mm, at least five tracks, and a vertex mass above 10 GeV — and count events at $L = 3$ ab$^{-1}$; more than a handful of events would invalidate the 3-event exclusions. For ANUBIS, the corresponding check is a complete background study of the service-shaft location, since its proximity to the IP could admit non-negligible backgrounds.

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Extended reading notes

Core claim

The central claim is that at the HL-LHC with $L=3\,\mathrm{ab}^{-1}$, displaced-vertex searches can probe dimension-six four-fermion operators containing a top quark and a heavy neutral lepton much more strongly than earlier estimates based on stable-HNL final states. For the pair-NR operator $\mathcal{O}^{13}_{uN}$, the dominant production is $pp \to tN\bar{N}$ in association with a top quark, and the HNL decays only through active-sterile mixing; the authors estimate that ATLAS can exclude scales $\Lambda \lesssim 12\,\mathrm{TeV}$ for $40\,\mathrm{GeV} \lesssim m_N \lesssim 80\,\mathrm{GeV}$ at $|V_{eN}|^2 = 10^{-10}$, while MATHUSLA (ANUBIS) reach about 4.5 (4) TeV for $m_N$ near 20 GeV. For single-NR operators such as $\mathcal{O}^{13}_{QuNL}$ and $\mathcal{O}^{13}_{duNe}$, the operator itself drives both production and decay, producing a funnel-shaped region of sensitivity where even negligibly small mixings are probed, and ATLAS reaches scales of 7 to 8 TeV. All reach estimates assume the vertex-level selection and far-detector shielding reduce backgrounds to zero, so the 95% exclusion is set at three signal events, with additional contours shown for ten or thirty events.

Load-bearing premise

The load-bearing premise is that the displaced-vertex selections at ATLAS and the shielding of the far detectors eliminate all Standard Model backgrounds, so three observed signal events suffice for a 95% confidence exclusion.

Editorial extensions

If this is right

If correct, the HL-LHC displaced-vertex program becomes a direct probe of top-philic HNL effective operators at scales an order of magnitude above present top-width limits.
For the pair-NR operator $\mathcal{O}^{13}_{uN}$, MATHUSLA and ANUBIS could reach active-sterile mixings as low as $|V_{eN}|^2 \sim 10^{-20}$ for $m_N \gtrsim 120$ GeV, far below current searches.
ATLAS and the far detectors cover complementary HNL mass ranges, so a combined analysis fills the mass-lifetime plane that neither experiment covers alone.
For single-NR operators, the funnel-shaped sensitivity means the operator alone can produce a displaced signal even with vanishing mixing, making the search sensitive to operators rather than only to mixing.
The flavor-diagonal variant $\mathcal{O}^{33}_{duNe}$ yields a weaker reach, at most about 1.5 TeV at ATLAS, so not all top-HNL operators are equally discoverable.

Reading between the lines

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

Editorial inference: the headline 12 (4.5) TeV reach rests on the zero-background premise; if a realistic Standard Model background simulation finds even a handful of events passing the lower jet-threshold selection, the 3-event contours would shrink, and the 10- or 30-event contours give a rough measure of that loss.
Editorial inference: the same search strategy could be applied to CMS or to data-parked low-threshold triggers, potentially delivering an independent cross-check and roughly doubling the ATLAS-like coverage.
Editorial inference: in the single-NR funnel regions a signal would not by itself determine the mixing parameter; measuring the HNL lifetime distribution or charge asymmetry would be needed to separate operator-induced from mixing-induced decays.
Editorial inference: the far-detector projections assume 100% detection efficiency, so folding in realistic tracking efficiencies would reduce the quoted far-detector scale reach proportionally to the efficiency.

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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

Here's my take: this is a well-executed projection study that breaks genuinely new ground by simulating displaced-vertex sensitivities for long-lived HNLs from d=6 top-quark operators. The headline numbers (Lambda ~ 12 TeV at ATLAS, 4.5 TeV at far detectors) are conditional on a zero-background assumption that the paper does not fully validate, but the paper is transparent about this and provides 10- and 30-event contours that largely defuse the worry.

The genuinely new content is the detector-level sensitivity study itself. The operator list and tree-level widths mostly come from Ref. [59], and the one-loop three-body decay reproduces Ref. [60], but the ATLAS low-threshold jet strategy and the far-detector acceptance calculations for these operators are new. I checked the derivations and they are coherent; the loop width is explicitly cross-checked against the literature. The benchmark scenarios are well chosen and the mass/mixing/scale structure of the results is clear.

The soft spot is exactly what the stress-test flags: the ATLAS contours are set by requiring 3 signal events because the authors assert that the vertex-level cuts suppress all backgrounds, but they lower the jet thresholds relative to the original 13 TeV search and provide no SM background estimate for the modified selection. If residual backgrounds appear, the reach shrinks roughly as (N_required/3)^{1/4} — 30 events would bring 12 TeV down to about 7 TeV. That said, the paper itself quotes the 10- and 30-event contours, so the reader is not misled. The far-detector 100% efficiency/zero-background assumptions are standard for these proposals, though optimistic. No code or model files are shipped, which is a minor drawback for reproducibility.

Overall, the central argument holds up: the projections are reasonable and the paper is careful. It is primarily for the HNL/LLP and EFT phenomenology community, and it deserves a serious referee. I'd recommend publishing after the authors add an explicit discussion of background robustness — even a simple scaling of the reach versus assumed background count, or a caveat on the 3-event contours, would be enough.

Referee Report

2 major / 4 minor

Summary. The paper studies long-lived heavy neutral leptons (HNLs) in the NRSMEFT, concentrating on dimension-6 four-fermion operators that couple HNLs to top quarks. Four benchmark scenarios are defined: the pair-NR operator O_uN^13 and the single-NR operators O_QuNL^13, O_duNe^13, and O_duNe^33. Production cross sections in pp collisions at 14 TeV and HNL decay widths (including a loop-induced three-body decay cross-checked against Ref. [60]) are computed, and the sensitivities of ATLAS and the far detectors MATHUSLA, ANUBIS, CODEX-b, and MAPP2 are estimated via displaced-vertex searches. The headline claim is that for O_uN^13 with c/Λ^2 = 1 TeV^-2, under zero-background and 100%-efficiency assumptions, ATLAS could probe scales up to Λ ≈ 12 TeV and MATHUSLA/ANUBIS up to Λ ≈ 4.5 TeV, with complementary HNL-mass coverage. The paper also provides 10- and 30-event contours to illustrate the impact of less optimistic assumptions.

Significance. If the projected sensitivities hold, the paper would establish a new and previously unstudied class of top-philic HNL operators as promising targets for HL-LHC displaced-vertex searches, with competitive scale reaches and complementary mass coverage between ATLAS and the far detectors. The paper is technically careful in several respects: the production and decay formulas are standard or cross-checked against the literature, the loop-induced three-body width is explicitly compared with Ref. [60], the ATLAS recast uses public parameterized efficiencies, and the far-detector geometry is implemented in detail. The authors are also transparent about the idealized nature of their event-count assumptions, and they show 10- and 30-event contours as a robustness check. However, the headline numbers quoted in the abstract and Section 4 are the 3-event, zero-background, 100%-efficiency projections, and these assumptions are not validated for the modified ATLAS selection or for the far-detector efficiencies. The significance is therefore real but conditional on assumptions that need further justification or a more cautious presentation.

major comments (2)

[Section 3.1, after Eq. (3.1), and footnote 13] The zero-background assumption for the proposed ATLAS DV+jets selection is load-bearing and currently unvalidated. The proposed selection lowers the jet-pT thresholds to 90/65/55 GeV and uses 4/5/6-jet multiplicities at 14 TeV, whereas the Run-2 search in Ref. [73] used harder selections; no SM background simulation is provided for the modified selection. Because the 3-event contours in Figs. 7 and 8 produce the abstract's Λ ≈ 12 TeV reach, even a small residual background could materially reduce the claimed exclusion power. For example, since the production rate scales roughly as Λ^-4 in the production-dominated regime, requiring 30 signal events instead of 3 would lower the Λ reach by about a factor of (3/30)^(1/4) ≈ 0.56, bringing 12 TeV to about 7 TeV. I ask the authors to either provide a background estimate for the modified selection or, in the abstract and Section 4, use the more robust 10- or 30-event contours as the primary stated reach, with the 3-event contours clearly labeled as idealized projections.
[Section 3.2, Eq. (3.3)] The far-detector sensitivity estimates assume ε = 100% detection efficiency and vanishing background, and the paper acknowledges this explicitly. This assumption is load-bearing for the quoted reach of Λ ≈ 4.5 TeV at MATHUSLA and ANUBIS, because reconstruction and selection efficiencies for HNL decays inside these detectors are not modeled. The 30-event contours provide some robustness against changes in acceptance or background level, but the abstract and Section 4 quote the 3-event, 100%-efficiency numbers as the primary results. Please either include more realistic efficiency assumptions or clearly present the far-detector numbers as upper-bound projections, with the efficiency dependence stated in the abstract and conclusions.

minor comments (4)

[Section 4 and abstract] The abstract's '12 TeV' reach is not explicitly derived in the text of Section 4, which states that ATLAS can probe scales 'in excess of 10 TeV' for 40 GeV ≲ m_N ≲ 80 GeV in scenario 1. Please specify the exact contour and parameter point that gives Λ ≈ 12 TeV, or adjust the abstract to match the stated numerical result.
[Eq. (3.1)] Please clarify whether the cross section σ in Eq. (3.1) is the sum over all relevant production channels and charge conjugates, e.g., pp → t N Nbar and pp → tbar N Nbar for the pair-NR case. The text discusses these channels separately, and an unambiguous normalization is important for reproducing the event counts.
[Section 4, upper-left panel of Fig. 7] The text says that MATHUSLA and ANUBIS reach HNL masses 'in excess of 1 TeV' and immediately adds that the plot range is limited by EFT validity for Λ = 1 TeV. Please reconcile these statements, since a reach above 1 TeV would appear to lie outside the valid region for the assumed Λ.
[Section 4, Fig. 8 caption] The caption for Fig. 8 states that solid lines correspond to |V_eN|^2 = 10^-10 except for scenario 2, where they correspond to 10^-9. This is consistent with footnote 18, but the main text would benefit from stating this exception in the same sentence where the mixing values are first introduced, to avoid apparent inconsistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the HL-LHC sensitivity projections are genuine model outputs from independently specified EFT parameters and published detector efficiencies.

full rationale

The paper's derivation chain is self-contained and does not reduce any predicted observable to a fitted input. The Wilson coefficients c/Λ^2, the active-sterile mixing |VeN|^2, and the HNL mass mN are scanned input parameters, not outputs fitted to the same data. Production cross-sections are computed from the EFT operators with MadGraph5, and decay widths are taken from published formulas in Refs. [59] and [70]; the one-loop three-body width is explicitly cross-checked against Ref. [60]. None of these inputs is normalized to reproduce the ATLAS, MATHUSLA, or ANUBIS reach contours that follow. The signal-count formulae, Eqs. (3.1) and (3.3), combine these inputs with efficiencies taken from the published ATLAS DV+jets search [73] and its recast [74]; those efficiencies are external experimental parameterizations, not fitted to the target exclusion curves. The 3-event threshold is a stated statistical criterion under an assumed zero-background condition, and the paper also provides 10- and 30-event contours, showing that the central result is not uniquely forced by a single normalization. Several references are authored by members of the present collaboration, notably Ref. [59] for top-decay widths, but these are externally published, parameter-free computations with stated assumptions, and their role here is the normal use of prior theoretical results rather than a load-bearing self-citation chain. The zero-background assumption for the proposed lower-threshold ATLAS selection is a physical fragility, not a circular step; it is an approximation that could weaken the quoted scales if backgrounds appear, but it does not amount to defining the prediction in terms of itself. No step of the type 'self_definitional', 'fitted_input_called_prediction', 'self_citation_load_bearing', 'uniqueness_imported_from_authors', 'ansatz_smuggled_in_via_citation', or 'renaming_known_result' could be exhibited from the text.

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

The ledger is dominated by scanned model inputs rather than fitted constants: mass, mixing, and operator coefficient define the axes of the sensitivity plots and are not learned from data. The genuine assumptions are the single-operator EFT benchmark, the electron-flavor-only simplification, and the background-free, 100-percent-efficiency experimental model. No new particle or mechanism is invented by this paper.

free parameters (3)

Active-sterile mixing |V_eN|^2 = not fitted; scanned from about 10^-20 to 10^-9 depending on scenario
Model input controlling HNL lifetime and mixing-induced decays; all sensitivity contours are drawn as functions of this parameter, so the quoted reaches are conditional on it. (Sections 2.3 and 4)
HNL mass m_N = not fitted; scanned up to about 1 TeV
Kinematic input scanned across the sensitivity plots; the reach in Lambda and |V_eN|^2 varies strongly with m_N. (Figures 7 and 8)
Operator coefficient c_ij^O / Lambda^2 = 1 TeV^-2 for all benchmark plots
Chosen to normalize the effective interaction; cross sections scale as (c/Lambda^2)^2, so the reported Lambda reaches are benchmark-dependent. (Section 2.3 and figure captions)

assumptions (4)

domain assumption New physics is fully described by the listed NRSMEFT d=6 four-fermion operators, with one operator switched on at a time and no SMEFT interference.
Section 2 parameterizes heavy states at scale Lambda with these operators, and each benchmark switches on a single operator; this excludes other new physics contributions to the same final states.
domain assumption One kinematically relevant HNL mixes only with electron neutrinos, and second-generation quark couplings are neglected.
Section 4 fixes V_lN = V_eN and states that muon results are expected to be similar; the flavor choice can affect decay channels and numerical reach.
ad hoc to paper SM backgrounds are fully suppressed by DV selections at ATLAS and are negligible at far detectors, with 100 percent detection efficiency in the latter.
Section 3.1 asserts that DV criteria suppress all backgrounds and sets 3-event exclusion thresholds; Section 3.2 assumes vanishing background and epsilon = 100 percent.
domain assumption Published ATLAS DV efficiencies and proposed far-detector geometries accurately represent the experiments.
Section 3 uses parameterized efficiencies from Ref. [73], detector sizes from MATHUSLA and ANUBIS proposals, and a simplified toy detector in Pythia; projections inherit any inaccuracies in these inputs.

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Cite this review

Pith. "Pith review of Heavy neutral leptons and top quarks in effective field theory." pith.science (2026). https://pith.science/paper/NDQTXEN5

@misc{pith2026250109065,
  author       = {Pith},
  title        = {Pith review of: Heavy neutral leptons and top quarks in effective field theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NDQTXEN5}},
  note         = {Machine review of arXiv:2501.09065}
}

abstract

We study the phenomenology of heavy neutral leptons (HNLs) at the LHC in effective field theory, concentrating on $d=6$ operators with top quarks. Depending on the operator choice and HNL mass, the HNLs will be produced either from proton-proton collisions in association with a single top, or via non-standard decays of top quarks. For long-lived HNLs we estimate the sensitivity reach of different detectors to various operators with top quarks and the HNLs for the high-luminosity phase of the LHC. For certain operators, ATLAS and some far detectors (MATHUSLA and ANUBIS) will be able to probe the associated new-physics scale as large as 12 TeV and 4.5 TeV, respectively, covering complementary HNL-mass ranges.

Discussion (0). Continue with ORCID to comment.

Forward citations

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