{"id":"a9a1a3dc-41be-4c0b-afed-e71b2bf6d24d","arxiv_id":"1908.02852","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Heavy neutrino searches at future ep colliders could reach mixing angles down to |θeθμ| ~ 10^-7 via lepton-trijet events and |θe|^2 ~ 10^-8 via displaced vertices.","lead":"This paper simulates how well two future electron-proton colliders, LHeC and FCC-he, could detect heavy sterile neutrinos through lepton-flavour-violating trijet and displaced vertex signatures. It concludes that these colliders could probe neutrino mixing angles far beyond current limits, making a strong physics case for building them.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Displaced-vertex exclusion contours rest on an untested zero-background assumption: the tau, B-meson and cosmic-muon vetoes plus the 40 micron vertex cut are asserted rather than simulated, so the Fig. 6 |theta_e|^2 reaches are upper bounds, not demonstrated projections.","rationale":"The reader identified the displaced-vertex background vetoes and the 40 micron vertex assumption as the weakest assumption. I agree that this is the most load-bearing concern in the paper's central claim. The abstract's superlative claim about the LFV lepton-trijet channel is supported by a reconstructed-level BDT analysis with explicit background samples and event counts, so it is less exposed. The DV reach in Fig. 6 and the Conclusions, however, is derived from an analytic decay-counting formula with zero background. The assumptions in Section 3.3.3 are explicit but unquantified: 'We assume that they can be effectively vetoed', 'We will assume that this allows for complete suppression', and 'we assume that the cosmic muons ... can be vetoed against effectively'. No efficiency or fake-rate inputs are given, and the Poisson threshold makes the result highly sensitive to even a single background event. A full detector-level check would either validate the contours or show upward shifts in the mixing-angle reach. Since the reader already rendered a CONDITIONAL verdict largely on this basis, my stress-test does not change the verdict.","tokens_in":15056,"tokens_out":20894,"duration_ms":243825,"concrete_test":"Run a GEANT4-level simulation of the LHeC detector for e-p -> nu nu j tau-, e-p -> nu b, e-p -> nu j b bbar, and cosmic-muon overlay events, applying the proposed tau-tag, B-mass veto, and a 40 micron 3D displaced-vertex reconstruction with realistic track-finding efficiency and fake rates. Count surviving background events in 1 ab^-1; if the expected background is above ~0.1 events, recompute the N_dv = 3.09 contour using a nonzero-background Poisson threshold and compare the resulting |theta_e|^2 curves with Fig. 6.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In the displaced-vertex analysis, the sensitivity contours are computed from Eq. (15)-(16), which counts only heavy-neutrino decays inside the detector volume; the 95% CL contour N_dv >= 3.09 is a pure Poisson threshold for zero background. Section 3.3.3 then assumes, without simulation, that tau leptons, B mesons and cosmic muons can be 'effectively vetoed' and that a 40 micron displacement suffices to identify a secondary vertex. These assumptions are load-bearing because the background-free threshold is very sensitive: with one expected background event the 95% CL signal threshold rises from 3.09 to about 5.3, a roughly 70% increase in required signal events, which shifts the |theta_e|^2 contours upward by a comparable factor. The paper gives no tau-tag efficiency, no B-tag fake rate, no cosmic-muon rejection factor, and no treatment of detector-material interactions, all of which are needed to justify the claimed O(10^-8) (LHeC) and O(10^-9) (FCC-he) reach. The lepton-trijet BDT analysis, by contrast, includes simulated backgrounds and quoted event counts; the DV part of the paper's central claim is the least secure.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the discovery and exclusion prospects for sterile (heavy) neutrinos in the symmetry-protected seesaw scenario (SPSS) at the proposed LHeC and FCC-he ep colliders. Two search channels are analysed: (i) a prompt lepton-flavour-violating trijet final state, p e− → μ− + 3j, simulated with MadGraph/Pythia/Delphes and separated from dominant vector-boson-pair backgrounds with a TMVA boosted decision tree (BDT); and (ii) a displaced-vertex search for mN < mW, where the number of signal vertices is estimated with Eqs. (15)–(16) using the full LHeC detector geometry and heavy-neutrino kinematic distributions. The paper reports 95% CL sensitivities |θeθμ| ≈ 10^-7 (FCC-he) and ≈ 2×10^-7 (LHeC) for mN around a few hundred GeV from the trijet channel, and |θe|^2 ≈ O(10^-8) (LHeC) and ≈ O(10^-9) (FCC-he) for mN < mW from displaced vertices. It further claims that, in the considered benchmark model, the LFV lepton-trijet channel gives the best sensitivity of all currently discussed heavy-neutrino signatures analysed at the reconstructed level.","tokens_in":15376,"tokens_out":10855,"duration_ms":123022,"significance":"If the results hold, the paper provides a valuable quantitative benchmark for heavy-neutrino searches at future ep colliders, a channel that is relatively unexplored compared to LHC searches. The prompt-trijet analysis is a genuine improvement over the earlier parton-level estimates of ref. [1]: it includes hadronization, detector simulation, several dominant backgrounds, a BDT with explicit train/test separation, quoted event counts at the working point, and expected 95% CL bands. The displaced-vertex analysis also improves on previous work by incorporating the asymmetric detector geometry and the full angular and boost distributions of the produced heavy neutrinos. The flavor dependence of the trijet limit is given explicitly. The main weakness is that the displaced-vertex reach relies on unvalidated zero-background assumptions, so the sub-mW contours in Fig. 6 are best regarded as optimistic projections until those assumptions are demonstrated or replaced by conservative background estimates.","major_comments":[{"comment":"The displaced-vertex exclusion contours are computed with a zero-background Poisson threshold (N_dv ≥ 3.09), but the background suppression on which this relies is asserted rather than demonstrated. The text assumes that tau leptons can be 'effectively vetoed against by existing tau tags', that B mesons allow 'complete suppression' via B-tag filters and a 5 GeV mass cut, and that cosmic muons 'can be vetoed against effectively' at displacements as small as 40 μm, but no tau-tag efficiency, B-tag fake rate, cosmic-muon rejection factor, or detector-material interaction estimate is provided. This is load-bearing: for example, the tau background alone has σ ≈ 0.34 pb, corresponding to about 3×10^5 events at 1 ab^-1 at the LHeC, and a qualitative statement that all such events can be vetoed is not quantitative. Even one surviving background event changes the 95% CL requirement from 3.09 signal events to roughly 3.7 under a standard Poisson construction, shifting the |θ_e|^2 contours in Fig. 6 upward by a comparable factor. Please either simulate these backgrounds with the same setup used for the prompt analysis or adopt conservative background counts and recompute the contours.","section":"Sec. 3.3.3, Eqs. (15)–(16), Fig. 6"},{"comment":"The assumed minimum vertex displacement of 40 μm is not validated for the signal final states. The text cites the LHeC CDR for tracking resolution, but the separation power at 40 μm depends on the track multiplicity, the material budget, and the boost distribution of the heavy neutrino; this quantity enters Eq. (16) through x_min(ϑ) and therefore directly controls the contours in Fig. 6. Please provide a vertexing demonstration based on a full simulation or a conservative scan (e.g., 100 μm) showing how the reach changes. Without this, the sub-mW displaced-vertex reach should be presented as an optimistic sensitivity estimate rather than a demonstrated projection.","section":"Sec. 3.3.2"}],"minor_comments":[{"comment":"Please specify how the 2% log-normal background systematic is implemented in the CLs/profile-likelihood calculation (e.g., as a single nuisance parameter on the total background after the BDT cut) and quantify its effect on the expected limit bands.","section":"Sec. 3.2.3, Fig. 5"},{"comment":"Please clarify whether the quoted production cross section and the simulated signal samples include Wγ-fusion in addition to t-channel W exchange; Eq. (7) as written describes t-channel exchange only.","section":"Sec. 3.1, Fig. 1"},{"comment":"The text states that the ~5% invisible N→3ν branching fraction is excluded, but Eq. (15) contains no explicit visible-branching prefactor. Please state where this factor enters the calculation.","section":"Eq. (15)"},{"comment":"The displaced-vertex sensitivities are quoted as limits on |θ_e θ_μ|, but Fig. 6 and the surrounding text define them as limits on |θ_e|^2 (with θ_μ = θ_τ = 0). Please correct the notation for consistency.","section":"Conclusions, first paragraph"},{"comment":"Ref. [38] appears in the bibliography but is not cited in the text; please cite it where relevant or remove it. Please also correct typographical errors: 'Ptyhia6' should be 'Pythia6' in Sec. 3.2.2; 'unless unless' appears in Sec. 3.4; and 'The LHeC makes utilizes' appears in Sec. 3.1.","section":"References and typos"}],"recommendation":"major_revision","confidential_remarks":"The prompt-trijet analysis is technically sound and publishable after minor clarifications. The displaced-vertex section needs substantial additional work or a conservative revision before the headline reach claims can be accepted. The 'best sensitivity of all currently discussed signatures' wording should also be checked against a broader survey before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing. The lepton-trijet analysis is a genuine step forward: first reconstructed-level, background-inclusive projection for this channel at LHeC and FCC-he, with hadronization, Delphes, a BDT with proper train/test separation, and quoted event counts. The resulting |θeθμ| reach of about 10^-7 (FCC-he) is credible and likely the best current projection for this specific signature. The displaced-vertex half is softer. The exclusion contours in Fig. 6 are computed from a zero-background Poisson threshold (N_dv >= 3.09). The claimed suppression of tau, B-meson, and cosmic-muon backgrounds is asserted in Section 3.3.3, not simulated; there is no tau-tag efficiency, B-tag fake rate, cosmic rejection factor, or material-interaction estimate, and the 40 micron vertex resolution is taken from the CDR without validation for this final state. One background event would shift the |θe|^2 contours up by roughly 70%, so the O(10^-8)/O(10^-9) reach figures are upper bounds, not demonstrated projections. The stress-test note lands on this correctly.\n\nWhat the paper does well: the prompt analysis is carefully executed and the statistical treatment (profile likelihood, 2% systematic) is standard and reasonable. The model setup is conventional for this community; the SPSS benchmark and symmetry limit are defensible. Production kinematics are discussed in useful detail, and the mass-dependence of the boost distributions is genuinely informative. The citation pattern leans on the authors' own earlier work, but that is appropriate because they are updating ref. [1]; the new analysis is not circular. No code or data is released, which is a minor limitation for reproducibility.\n\nSoft spots: the DV background assumption is load-bearing. The 'best sensitivity of all currently discussed signatures' sentence is broader than the channels actually analysed; it is fine for the lepton-trijet channel but should be qualified. The b-jet mass veto around 5 GeV is not quantified. These are fixable in revision.\n\nWho this is for: phenomenologists working on sterile neutrino searches and members of LHeC/FCC-he collaborations. It deserves a serious referee. I would send it to review and ask for a revision that either simulates the DV backgrounds or explicitly frames the DV curves as background-free upper bounds with the required veto efficiencies stated. As is, the lepton-trijet part stands on its own; the DV part needs more evidence.","headline":"Solid lepton-trijet projection for sterile neutrinos at ep colliders; the displaced-vertex reach is plausible but rests on an unquantified zero-background assumption.","tokens_in":15833,"tokens_out":3020,"would_cite":false,"duration_ms":31912,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper projects that the lepton-flavour-violating trijet channel at electron-proton colliders can exclude $|\\theta_e\\theta_\\mu| \\sim 10^{-7}$ at 95% CL, the best reconstructed-level sensitivity claimed for heavy neutrinos in this mass…","keywords":["heavy neutrinos","sterile neutrinos","electron-proton colliders","LHeC","FCC-he","lepton flavour violation","displaced vertices","seesaw mechanism"],"falsifier":"Recompute the displaced-vertex background with explicit veto inefficiencies rather than perfect suppression: if tau-tag inefficiency or B-meson mass-window leakage leaves more than about three background events in the signal region at $1\\,{\\rm ab}^{-1}$, the claimed 95% CL $|\\theta_e|^2$ contours for $m_N$ below $m_W$ would shift upward by roughly an order of magnitude. A direct way to check this is a background-only data sample at an ep detector that records any displaced tau or B decay inside the 40-micrometre window.","tokens_in":14860,"feed_emoji":"⚛️","tokens_out":11102,"duration_ms":107360,"temperature":0.7,"pith_summary":"The paper argues that future electron-proton colliders would be particularly effective at discovering sterile heavy neutrinos with masses near the electroweak scale. In the symmetry-protected seesaw benchmark model it adopts, the lepton-flavour-violating process $p e^- \\to \\mu^- + 3j$ has no parton-level Standard Model counterpart, and a reconstruction-level analysis with a boosted decision tree projects 95% CL exclusions of $|\\theta_e\\theta_\\mu|$ down to about $2\\times 10^{-7}$ at the LHeC and $10^{-7}$ at the FCC-he for masses of a few hundred GeV. For lighter masses below the $W$ mass, displaced-vertex decays are projected to reach $|\\theta_e|^2$ of order $10^{-8}$ at the LHeC and $10^{-9}$ at the FCC-he. If these estimates hold, ep colliders would probe a region of active-sterile mixing that present constraints leave open.","feed_headline":"Lepton-trijet searches at ep colliders could hit 10^-7 mixing","feed_subtitle":"Prompt trijets and displaced vertices would probe mixings below current experiment limits.","key_machinery":"The analysis is carried by the active-sterile mixing parameters $\\theta_\\alpha$ and the process chain $p e^- \\to N + j$ with $N \\to \\mu^- W^+ \\to \\mu^- jj$, whose rate scales as $|\\theta_e|^2|\\theta_\\mu|^2/|\\theta|^2$; under the benchmark choice $|\\theta_e| = |\\theta_\\mu|$ this reduces to $|\\theta_e\\theta_\\mu|$. For the prompt search, a boosted decision tree trained on 18 kinematic distributions—including the reconstructed heavy-neutrino invariant mass, muon transverse momentum, missing transverse energy, and angular separations between the $W$, the muon, and the beam jet—separates signal from backgrounds. For the displaced-vertex search, the machinery is the decay probability $P_{\\rm dv} = \\exp(-x_{\\min}/\\Delta x_{\\rm lab}) - \\exp(-x_{\\max}/\\Delta x_{\\rm lab})$, integrated over the full production angular and Lorentz-boost distributions and the asymmetric detector geometry, with a 95% CL exclusion set at $N_{\\rm dv} \\ge 3.09$ expected decays.","core_discovery":"Working in the symmetry limit of the SPSS benchmark model, where two sterile neutrinos form a pair with opposite charges under a lepton-number-like symmetry and lepton number is conserved, the authors show that two signatures dominate the expected reach at ep colliders. The prompt lepton-trijet channel, $p e^- \\to N j \\to \\mu^- W^+ j \\to \\mu^- + 3j$, is free of irreducible Standard Model background at parton level; once the dominant backgrounds are included and a boosted decision tree is optimized, the expected 95% CL limits reach $|\\theta_e\\theta_\\mu| \\approx 2\\times 10^{-7}$ at the LHeC and $\\approx 10^{-7}$ at the FCC-he for heavy-neutrino masses of a few hundred GeV. For masses below $m_W$, where the heavy neutrino can travel a macroscopic distance before decaying, the displaced-vertex channel reaches $|\\theta_e|^2 \\sim 10^{-8}$ at the LHeC and $\\sim 10^{-9}$ at the FCC-he. The paper concludes that, in this mass range, the LFV lepton-trijet signature yields the best sensitivity of all currently discussed heavy-neutrino signatures analysed at the reconstructed level.","pith_inferences":["Beyond the paper's claims, if the displaced-vertex reach holds up under a more realistic background treatment, ep colliders would be the most direct way to test low-scale seesaw masses below $m_W$, where hadron colliders lose sensitivity to small mixings.","The strong mass dependence of the reconstructed kinematic distributions suggests that a heavy-neutrino mass could be inferred from shapes alone; the paper notes this only in passing, and a dedicated shape-based measurement would be a natural extension.","A testable extension would drop the protective symmetry and repeat the analysis with a single sterile neutrino, restoring lepton-number-violating decays; the change in the trijet reach would quantify how much of the projected sensitivity relies on the symmetry limit.","Applying the same search pipeline to a $\\tau^-jjj$ final state with realistic tau-tagging efficiencies would test whether the paper's golden-channel claim survives reconstruction losses for taus."],"forward_implications":["In the few-hundred-GeV mass region, the LFV trijet channel is projected to probe $|\\theta_e\\theta_\\mu|$ values an order of magnitude or more below current exclusion limits.","The displaced-vertex channel covers the sub-$m_W$ mass range from about 5 GeV upward with $|\\theta_e|^2$ reach of $10^{-8}$ to $10^{-9}$, a region where prompt searches lose sensitivity to small mixings.","Because the signature rate depends on the flavour combination $2|\\theta_e|^2|\\theta_\\mu|^2/|\\theta|^2$, the results transfer to other flavour patterns, such as a $\\tau^- jjj$ final state when muon mixing is small.","Within the displaced-vertex contour, the lepton-number-conserving framework also allows an anti-lepton version of the trijet final state, whose oscillatory lifetime dependence could reveal heavy-neutrino-antineutrino oscillations and, with enough statistics, a measurement of the mass splitting."],"supporting_citations":[{"why":"Supplies the earlier parton-level sensitivity estimates for heavy-neutrino signatures at ep colliders that this paper improves to reconstruction level.","marker":"[1]"},{"why":"Defines the symmetry-protected seesaw benchmark model and the active-sterile mixing parametrisation used throughout.","marker":"[7]"},{"why":"Provides the LHeC detector description, interaction-region size, tracking resolution, and the 40-micrometre secondary-vertex displacement criterion.","marker":"[10]"},{"why":"Provides the Monte Carlo event generator used to produce signal and background samples before showering and detector simulation.","marker":"[29]"},{"why":"Supplies the boosted decision tree implementation used to separate the trijet signal from backgrounds.","marker":"[33]"},{"why":"Supplies the statistical tool used to derive 95% CL expected limits from the remaining signal and background event counts.","marker":"[34]"},{"why":"Provides the displaced-vertex decay probability formalism used to count expected secondary vertices.","marker":"[36]"},{"why":"Supplies the current displaced-vertex search exclusion limit used as a comparison in the sensitivity plots.","marker":"[6]"},{"why":"Supplies the current flavour constraint on the same mixing combination, used as a benchmark for comparison in the sensitivity plots.","marker":"[37]"}],"fun_headline_variants":["Lepton-trijet searches at future ep colliders hit 1e-7 mixing","Trijet channel yields best heavy neutrino sensitivity at ep colliders","Displaced vertex searches at FCC-he probe 1e-9 neutrino mixing","ep colliders: lepton trijets reach 1e-7 mixing, displaced vertices 1e-9","Future ep colliders: trijets to 1e-7, displaced vertices to 1e-9"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The displaced-vertex reach assumes that tau leptons, B mesons, and cosmic muons can be completely suppressed by the stated vetoes and mass cuts, and that a displacement of 40 micrometres is enough to identify a secondary vertex; if any of those vetoes leaks events, the projected $|\\theta_e|^2$ contours move to larger mixing angles.","fun_headline_variants_meta":{"raw":{"variants":["Lepton-trijet searches at future ep colliders hit 1e-7 mixing","Trijet channel yields best heavy neutrino sensitivity at ep colliders","Displaced vertex searches at FCC-he probe 1e-9 neutrino mixing","ep colliders: lepton trijets reach 1e-7 mixing, displaced vertices 1e-9","Future ep colliders: trijets to 1e-7, displaced vertices to 1e-9"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000546,"raw_usage":{"total_tokens":2613,"prompt_tokens":948,"completion_tokens":1665,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":564,"completion_tokens_details":{"reasoning_tokens":1550}},"tokens_in":564,"tokens_out":1665,"duration_ms":14108,"temperature":1.0,"reasoning_tokens":1550,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:32:02.004794+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the displaced-vertex background with explicit veto inefficiencies rather than perfect suppression: if tau-tag inefficiency or B-meson mass-window leakage leaves more than about three background events in the signal region at $1\\,{\\rm ab}^{-1}$, the claimed 95% CL $|\\theta_e|^2$ contours for $m_N$ below $m_W$ would shift upward by roughly an order of magnitude. A direct way to check this is a background-only data sample at an ep detector that records any displaced tau or B decay inside the 40-micrometre window.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the statistical tool used to derive 95% CL expected limits from the remaining signal and background event counts."}],"review_version":1}