{"id":"20b0cb82-859b-41ab-ba97-e1affc59aed7","arxiv_id":"2412.07125","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Projected 5-sigma discovery regions for singlet vector-like leptons at the 1 TeV ILC are derived, covering masses 300-700 GeV and coupling kappa down to about 0.026.","lead":"This paper asks whether a proposed future electron-positron collider, the ILC, could spot a new heavy 'cousin' of the electron that some theories predict. It simulates the collisions and finds that such a particle could be detected if it weighs between 300 and 700 GeV and couples to ordinary matter with a strength above a narrow range.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The quoted 5σ reach rectangles are inconsistent with the paper's own cut-based significance tables: at MF=600, κ=0.03 gives SS=0.0029 (leptonic) and 0.0068 (hadronic), so even κ=0.1 cannot approach 5σ.","rationale":"The Reader's conditional verdict focused on the ambiguity between κ being an independent scan parameter and κ being fixed by the muon g-2 constraint. That is a legitimate concern, but the more decisive problem is internal: even granting the paper's independent κ scan, the stated detection regions are contradicted by the paper's own significance tables. Because S scales as κ^2 and B is fixed, the high-mass entries in Tables II and IV imply that κ must be of order 1 to reach 5σ at MF≈600-700 GeV, not κ≈0.03-0.1. Therefore the 5σ contours in Fig. 5 and the abstract/conclusion rectangles cannot be derived from the presented simulation results as written. This is not a missing systematic uncertainty or a stylistic issue; it is a direct inconsistency in the central quantitative claim. A reanalysis with consistent reach curves would likely shrink the detectable parameter space dramatically, so the appropriate action is to reject the current version rather than accept it conditionally pending minor clarifications. I emphasize that this is a critique of the argument and numbers, not of the authors; the simulation chain itself is standard and reproducible in principle, but the reported reach extraction needs to be redone and explained.","tokens_in":11459,"tokens_out":13036,"duration_ms":132129,"concrete_test":"Recompute the 5σ reach curves from Tables II and IV: for MF=400, 500, 600, and 700 GeV, use the post-cut signal cross sections S0 and background B from the tables with L=1 ab^-1, and solve SS = S0·(κ/0.03)^2 / sqrt(S0·(κ/0.03)^2 + B) = 5 for κ. Compare the resulting κ5σ(MF) values with the 5σ contour in Fig. 5. The expected values are κ5σ(600 GeV)≈1.26 (leptonic) and ≈0.82 (hadronic), and κ5σ(700 GeV)≈3.5 and ≈2.2, respectively; if these hold, the published reach rectangles must be revised downward substantially.","verdict_should_be":"REJECT","load_bearing_attack":"The central claim in the Abstract and Conclusions — 5σ reach up to MF=675 GeV (pure leptonic) and MF=700 GeV (fully hadronic) for κ≤0.1 — cannot be reproduced from the paper's own Tables II and IV. For a fixed MF, the signal rate scales as κ^2, while the background and branching ratios are κ-independent, so the rescaled significance after the quoted cuts is SS(MF,κ)=SS(MF,0.03)·(κ/0.03)^2, with S<<B for the high-mass points so the scaling is effectively exact. Using Table II (pure leptonic): at MF=600 GeV, after all cuts S=2.2701e-7 pb and B=6.1029e-3 pb give SS=0.00291 at κ=0.03; reaching SS=5 would require S≈403 events, i.e. κ≈1.26, far outside the quoted κ∈[0.0294,0.1]. At MF=700 GeV the required κ is even larger. For the fully hadronic channel, Table IV at MF=600 GeV gives SS=0.00683; the 5σ requirement S≈805 events forces κ≈0.82, and at MF=700 GeV κ≈2.24. Thus the rectangles in the Abstract and Conclusions, and the corresponding 5σ contours in Fig. 5, are incompatible with the paper's own Monte Carlo tables unless an unstated alternative procedure was used to produce Fig. 5. This is an internal inconsistency in the main quantitative claim, independent of the κ/κ′ g-2 ambiguity noted by the Reader.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies the single production of singlet vector-like leptons (VLLs) in the scalar-extended VLS model at a 1 TeV ILC with 1 ab^-1 and polarization P(e+, e-) = (-30%, 80%). It considers W-boson decays in the pure leptonic channel (two charged leptons plus missing energy) and the fully hadronic channel (two jets, one charged lepton, missing energy), using a MadGraph5/Pythia8/Delphes3/MadAnalysis5 pipeline. The authors present a cut-based analysis with cross sections after each cut and statistical significances, and they claim 5 sigma discovery reach for MF in [300, 675] GeV with kappa in [0.0294, 0.1] (leptonic) and MF in [300, 700] GeV with kappa in [0.0264, 0.0941] (hadronic).","tokens_in":11764,"tokens_out":11475,"duration_ms":109867,"significance":"If the quoted reach were correct, the paper would provide a useful projection for singlet VLL searches at the ILC and a concrete benchmark for the VLS model. The paper has clear strengths: the simulation chain is standard and reproducible, the cut flow is transparent with cross sections per cut in Tables II and IV, the polarization choice is motivated by a cross-section scan, and the significance formula is stated explicitly. The main weakness is that the headline reach regions are not supported by the paper's own Monte Carlo tables; the 5 sigma contours in Fig. 5 and the Abstract/Conclusions are internally inconsistent with the numerical significances in Tables II and IV. This makes the central quantitative claim unreliable in its present form.","major_comments":[{"comment":"The claimed 5 sigma reach rectangles cannot be reproduced from the paper's own cut tables. For the pure leptonic channel, Table II for MF = 600 GeV and kappa = 0.03 gives S = 2.2701 x 10^-7 pb and B = 6.1029 x 10^-3 pb, i.e. 0.227 signal events and 6103 background events at 1 ab^-1, corresponding to SS = 0.00291 as listed. Since the signal rate scales as kappa^2 while the background is kappa-independent, kappa = 0.1 gives only SS ~ 0.032; reaching SS = 5 at MF = 600 would require kappa ~ 1.24, far outside the quoted interval [0.0294, 0.1]. The same check on the fully hadronic channel using Table IV gives S = 1.0786 events and B = 25100 events at MF = 600 and kappa = 0.03 (SS = 0.00683); SS = 5 would require kappa ~ 0.81, and at MF = 700, kappa ~ 2.2. Thus the Abstract's MF in [300, 675] GeV (leptonic) and MF in [300, 700] GeV (hadronic) ranges, and the corresponding 5 sigma curves in Fig. 5, are incompatible with the stated cut-based analysis. This is not a minor scaling issue but a contradiction in the main quantitative result, and it must be resolved by recomputing the reach or by explaining an unstated alternative procedure.","section":"Abstract and Conclusions vs. Tables II and IV"},{"comment":"The role of the muon anomalous magnetic moment constraint in the parameter scan is ambiguous and load-bearing for the two-dimensional reach plots. The text says that kappa-prime can be expressed in terms of MF and MS via Eq. (6), and then fixes kappa/kappa-prime = 10^-2 with kappa-prime computed from Eq. (6) for MS = 500 GeV while scanning kappa in (0.01, 0.1). If kappa-prime is indeed fixed by the g-2 constraint for each MF, then kappa = 10^-2 kappa-prime is also determined as a function of MF, and the (MF, kappa) plane collapses to a one-dimensional curve; the filled rectangles in the Abstract and Fig. 5 would then overstate the independent parameter space. If instead kappa is meant to be an independent input in (0.01, 0.1), then Eq. (6) cannot be enforced simultaneously for all scanned points unless kappa-prime is also scanned and the AMM anomaly is not necessarily explained. The authors should state unambiguously which procedure generated Fig. 5; without this, the physical interpretation of the quoted kappa ranges is unclear.","section":"Section II, Eqs. (1)-(6)"}],"minor_comments":[{"comment":"The Abstract calls the results 'analytic results' although they are obtained from a Monte Carlo detector-level simulation; 'simulation results' or 'numerical results' would be more accurate.","section":"Abstract"},{"comment":"There are typos: 'electroweak symmertry breaking' and 'asymptotically safety' should read 'electroweak symmetry breaking' and 'asymptotic safety'.","section":"Section II"},{"comment":"The SS row of both tables has broken spacing (e.g., '3 .541', '0 .479', '7 .6531'); the typesetting should be corrected.","section":"Table II and Table IV"},{"comment":"In the discussion of Fig. 3(c) and (d), the sentence 'the SM background has a peak at low values for eta_l-' is followed by 'while the SM background has a peak at high values for eta_l+'; the second clause should refer to the signal distribution.","section":"Section III A"},{"comment":"The variable written as 'Mef f' should be typeset as M_eff or similar, and its definition should appear consistently in the text and figure captions.","section":"Section III B"}],"recommendation":"major_revision","confidential_remarks":"The stress-test concern is confirmed: the headline 5 sigma reach regions in the Abstract, Conclusions, and Fig. 5 cannot be obtained from Tables II and IV under the stated kappa^2 scaling, and the g-2/kappa scan ambiguity in Section II further obscures the meaning of the two-dimensional contours. I would ask the authors to recompute the reach with a clearly specified parameter treatment and to reframe the conclusions accordingly; the underlying simulation chain is sound and the per-cut cross-section tables are useful, so a corrected version could be publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear Colleague,\n\nThe paper is a standard MadGraph/Delphes projection study for single production of singlet vector-like leptons at the ILC. The new pieces are the use of beam polarization P(e+,e−)=(−30%,80%) at 1 TeV and the separate treatment of pure leptonic and fully hadronic W decay channels. The simulation chain is normal for this field, the cut flows are clearly described, and the tables of cross sections at each cut are transparent. I believed the numbers until I checked them.\n\nThe problem is that the abstract's and conclusions' 5σ reach rectangles do not follow from the paper's own Tables II and IV. At κ=0.03, the signal after all cuts at MF=600 GeV is 2.27×10⁻⁷ pb (leptonic) and 1.08×10⁻⁶ pb (hadronic), with backgrounds of 6.10×10⁻³ pb and 2.51×10⁻² pb. That gives SS ≈ 0.003 and 0.007 respectively. Since the signal scales as κ² and the background is κ-independent, even κ=0.1 gives SS of order 0.03 and 0.08. The 5σ curves in Fig. 5 and the rectangles in the abstract therefore cannot be reproduced from the quoted numbers unless an unstated procedure was used. This is not a minor rounding issue; the claimed reach up to MF=675–700 GeV with κ~0.03–0.1 is off by orders of magnitude in significance. The paper needs to show explicitly how Fig. 5 was generated, or correct the abstract and figures.\n\nThere are two other, smaller problems. The text says κ′ is fixed by the muon g−2 via Eq. (6) while κ is scanned independently, but then states κ/κ′=10⁻². If κ′ is determined by g−2, κ is fixed for each MF, and the 2D region collapses to a curve; if κ is free, the g−2 constraint is not being imposed. The authors need to clarify. Also, Eq. (5) is dimensionally inconsistent (the right-hand side is dimensionless, not mass⁻²); likely a typo, since the MadGraph results are presumably correct.\n\nIf these issues can be fixed, the paper could be a useful projection for ILC planning. As it stands, the central quantitative claim is unsupported by the paper's own data. I would send it to peer review, because the methodology is sound and the inconsistency is likely fixable, but I would not cite it until the numbers are reconciled.","headline":"The 5σ reach rectangles claimed in the abstract do not follow from the paper's own cut tables; the significance is off by orders of magnitude at high mass.","tokens_in":12359,"tokens_out":4569,"would_cite":false,"duration_ms":43792,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"At a 1 TeV electron-positron collider, single production of singlet vector-like leptons could be detected at 5σ for masses up to about 700 GeV, with the fully hadronic W-decay channel giving the larger reach.","keywords":["vector-like leptons","singlet VLS model","International Linear Collider","single production","muon anomalous magnetic moment","polarized beams","leptonic decay channel","hadronic decay channel"],"falsifier":"Recompute the $5\\sigma$ contours with $\\kappa$ fixed by Eq. (6) and the relation $\\kappa/\\kappa' = 10^{-2}$ at $M_S = 500$ GeV for each $M_F$; if the resulting curve never reaches $5\\sigma$ inside the quoted mass range, the paper's central quantitative claim fails.","tokens_in":11182,"feed_emoji":"⚛️","tokens_out":17375,"duration_ms":137640,"temperature":0.7,"pith_summary":"This paper argues that a proposed 1 TeV International Linear Collider (ILC) with polarized beams and 1 ab$^{-1}$ of data could discover the singlet vector-like leptons predicted by the vector-like-lepton-with-scalar (VLS) model. The authors compute the cross section for single production $e^+e^- \\to \\psi\\ell$, let the VLL decay through $\\psi \\to W\\nu$, and consider two $W$ decay modes: pure leptonic (two charged leptons plus missing energy) and fully hadronic (two jets, one lepton, and missing energy). They find $5\\sigma$ sensitivity for a mass window $M_F \\in [300, 675]$ GeV and coupling $\\kappa \\in [0.0294, 0.1]$ in the leptonic channel, and a larger window $M_F \\in [300, 700]$ GeV with $\\kappa \\in [0.0264, 0.0941]$ in the hadronic channel. The fully hadronic channel is the more sensitive of the two. The point of the exercise is that a future lepton collider can probe this class of new fermions more cleanly than a hadron collider, giving a concrete experimental target for the VLS model.","feed_headline":"1 TeV ILC could detect vector-like leptons up to 700 GeV","feed_subtitle":"Polarized beams and two W-decay channels give 5σ sensitivity for masses 300–700 GeV and couplings down to about 0.026.","key_machinery":"The argument is carried by the singlet VLS model and the single-production process it generates. The model adds to the Standard Model a generation of SU(2)-singlet vector-like leptons $\\psi$ and a new scalar $S$, with Yukawa couplings $\\kappa$ and $\\kappa'$ to the Higgs $h$ and $S$, respectively. After electroweak symmetry breaking, these couplings induce effective $\\psi$–$Z$ and $\\psi$–$W$ interactions whose strength scales as $\\kappa v / M_F$; these drive the s-channel production $e^+e^- \\to \\psi\\ell$ via $Z$ exchange (Eq. (5)) and the decay $\\psi \\to W\\nu,\\, Z\\ell,\\, h\\ell$. The analysis machinery is a cut-based collider study: Monte Carlo event generation at leading order, parton showering and hadronization, fast detector simulation with the ILD detector card, and a statistical significance evaluated as $S/\\sqrt{S+B}$ after kinematic cuts on missing energy, transverse energy, and pseudorapidity of the leptons (or on $M_{\\rm eff}$ and $E_T$ for the hadronic channel). The model assumption that $\\kappa/\\kappa' = 10^{-2}$ with $\\kappa'$ fixed by the muon anomalous magnetic moment (Eq. (6)) at $M_S = 500$ GeV anchors the coupling to the experiment that motivates the model.","core_discovery":"The central discovery claim is that, within the singlet VLS model, the process $e^+e^- \\to \\psi\\ell$ followed by $\\psi \\to W\\nu$ and $W \\to \\ell\\nu$ or $jj$ yields a statistically significant signal at the ILC. With $\\sqrt{s} = 1$ TeV, $L = 1$ ab$^{-1}$, and beam polarization $P(e^+, e^-) = (-30\\%, 80\\%)$, the $5\\sigma$ contours in the ($M_F$, $\\kappa$) plane enclose $M_F$ from 300 to 675 GeV and $\\kappa$ from 0.0294 to 0.1 for the pure leptonic channel, and $M_F$ from 300 to 700 GeV with $\\kappa$ from 0.0264 to 0.0941 for the fully hadronic channel. The fully hadronic channel reaches significance 13.06 at $M_F = 300$ GeV and 7.65 at $M_F = 400$ GeV for $\\kappa = 0.03$, compared with 6.28 and 3.54 in the leptonic channel. The paper's bottom line is that the ILC could either discover or exclude singlet vector-like leptons in most of the mass range below 700 GeV, provided the coupling $\\kappa$ lies above about 0.026.","pith_inferences":["The two-dimensional reach regions treat κ and MF as independent parameters, but the model's own muon-g-2 constraint (Eq. (6) with κ/κ′ = 10^-2 at MS = 500 GeV) may fix κ for each MF; if so, the accessible parameter space collapses to a one-dimensional curve and the quoted rectangles likely overstate the discovery region.","The quoted boundaries are derived from leading-order event generation; higher-order QCD and electroweak corrections could shift the signal and background shapes and move the 5σ contours by of order ten to twenty percent.","The same single-production search strategy transfers directly to other proposed lepton colliders with adapted luminosity and energy, so the method generalizes beyond the specific ILC parameters assumed here.","If the muon g-2 anomaly is later resolved by different new physics, the preferred values of κ and κ′ would change, and the reach regions would need to be recomputed; the discovery claim is contingent on the g-2 interpretation."],"forward_implications":["A null result at the 1 TeV ILC with 1 ab^-1 would exclude singlet vector-like leptons with masses below about 700 GeV and couplings κ down to roughly 0.026 in the VLS model, given the assumed polarization.","The fully hadronic W-decay channel should be the primary search mode at lepton colliders, since it yields a larger reach in both MF and κ than the pure leptonic channel.","The chosen beam polarization P(e+, e-) = (−30%, 80%) enhances the single-production cross section and suppresses the dominant electroweak backgrounds, making it a key ingredient of the projected sensitivity.","Because the single-production cross sections are nearly identical for the first, second, and third generations of VLLs, the same search applies to all three generations without modification.","If no signal appears, the ILC measurement would directly probe the coupling region that the VLS model invokes to explain the muon g-2 anomaly, providing a cross-check of that explanation."],"supporting_citations":[{"why":"Defines the singlet VLS model Lagrangian and the Yukawa couplings κ and κ′ on which the production and decay amplitudes are built.","marker":"[41]"},{"why":"Derives the muon anomalous-magnetic-moment contribution ∆aµ (Eq. (6)) used to fix κ′ from the g-2 anomaly, anchoring the scan over κ.","marker":"[42]"},{"why":"Provides the branching ratios of the singlet vector-like lepton decays that select Wν as the dominant channel to search for.","marker":"[49]"},{"why":"Reports the experimental muon g-2 measurement whose deviation from the Standard Model motivates the VLS model and sets the coupling scale.","marker":"[9]"},{"why":"Supplies the Monte Carlo event generator used to compute the leading-order signal and Standard Model background samples.","marker":"[58]"},{"why":"Supplies the fast detector simulation with the ILD detector card used to model the ILC detector response.","marker":"[61]"},{"why":"Specifies the ILC baseline of 1 TeV center-of-mass energy and 1 ab^-1 integrated luminosity assumed throughout the study.","marker":"[54]"}],"fun_headline_variants":["1 TeV ILC could spot vector-like leptons up to 700 GeV","Polarized ILC may reveal heavy leptons below 700 GeV","ILC's 1 TeV run could expose new leptons to 700 GeV","Vector-like leptons reach to 700 GeV at ILC","ILC could see singlet leptons up to 700 GeV"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis scans the coupling $\\kappa$ freely at each mass, assuming $\\kappa$ and $M_F$ are independent, even though the model's muon-g-2 constraint may tie $\\kappa$ to $M_F$ and collapse the quoted two-dimensional discovery regions to a curve.","fun_headline_variants_meta":{"raw":{"variants":["1 TeV ILC could spot vector-like leptons up to 700 GeV","Polarized ILC may reveal heavy leptons below 700 GeV","ILC's 1 TeV run could expose new leptons to 700 GeV","Vector-like leptons reach to 700 GeV at ILC","ILC could see singlet leptons up to 700 GeV"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001366,"raw_usage":{"total_tokens":5604,"prompt_tokens":1074,"completion_tokens":4530,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":690,"completion_tokens_details":{"reasoning_tokens":4432}},"tokens_in":690,"tokens_out":4530,"duration_ms":31374,"temperature":1.0,"reasoning_tokens":4432,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T19:06:53.280865+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the $5\\sigma$ contours with $\\kappa$ fixed by Eq. (6) and the relation $\\kappa/\\kappa' = 10^{-2}$ at $M_S = 500$ GeV for each $M_F$; if the resulting curve never reaches $5\\sigma$ inside the quoted mass range, the paper's central quantitative claim fails.","supporting_citations":[{"cited_title":"Multi-lepton signatures of vector-like leptons with flavor","cited_arxiv_id":"2011.12964","evidence_quote":"Provides the branching ratios of the singlet vector-like lepton decays that select Wν as the dominant channel to search for."}],"review_version":1}